Australia, who had lost 1-2 to France in their opening match, got their goal from a penalty conversion by captain Mile Jedinak in the 38th minute after Denmark had taken a 1-0 lead through Christian Eriksen in the seventh minute.
Earlier in the match, Denmark star player Christian Eriksen linked up well with Nicolai Jorgensen to smash a half-volley past Mat Ryan in the 7th minute, opening up what looked to be a match almost certainly dominated by the Danes, reports Efe.
But the Aussies struck back earning a penalty when Yussuf Poulsen blocked a cross with his hand, taking a yellow card in the process.
Mile Jedinak dutifully stepped up to the spot and slotted it to the right-hand-side of the net, sending Kasper Schmeichel the wrong way.
Australia was quick out the blocks after half-time but failed to cash in on the promise its attacking display showed.
The game ground to a draw, meaning Denmark head into its final group game with four points while Australia have just one.
An own goal from Thiago Cionek in the 37th minute and a quick counter-attack goal from M'Baye Niang in the 60th minute gave Senegal the 2-0 lead. Poland pulled one back through Grzegorz Krychowiak but it was late for the European team to find an equaliser.
"We are very disappointed by the defeat," Saudi Football Federation chief Adel Ezzat was quoted as saying by the Al-Youm Assabaa newspaper, reports Tass news agency.
"This result is totally unsatisfactory because it does not reflect the true level of our preparedness.
"Several players will face a penalty - goalkeeper Abdullah Al-Mayouf, striker Mohammad Al-Sahlawi and defender Omar Hawsawi," he added.
The Chairman of the General Sport Authority, Turki bin Abdulmohsen Al-Sheikh, described the game as a "total fiasco" in a video address, posted on his Twitter page.
The 2018 FIFA World Cup kicked off on Thursday with the opening match in the Russian capital Moscow between hosts Russia and the national team from Saudi Arabia, which Russia won 5-0.
In its next game, Saudi Arabia is facing Uruguay in the southern Russian city of Rostov-on-Don on June 20.
Yuri Gazinskiy (12th minute), Denis Cheryshev (43rd, 90+1), Artem Dzyuba (71st) and Aleksandr Golovin (90+4) scored for the hosts, who enjoyed a near-perfect first day.
They overcame the injury suffered by forward Alan Dzagoev in the middle of the first half. But his substitute Cheryshev scored a brace and young Golovin made two assists and a goal to more than make up for Dzagoev's absence.
Russia were impressive from the beginning and threatened the Saudis with fierce counter-attacks. Russia employed pressure by earning multiple corners and after one of them was blocked, Russia regained the ball. Aleksandr Golovin fired in a beautiful cross from right to the centre of the box from where Yuri Gazinskiy headed it in at the left post past Abdullah Mayoof to make it 1-0.
Four minutes later, off another counter-attack, Alan Dzagoev delayed his shot, allowing Mohammed Alburayk to block but the ball deflected before being parried away by Mayoof.
Saudi Arabia got their first chance at goal when Mohammed Al Sahlawi's left footed shot from the left side of the box went inches wide.
Russia later suffered a big blow as Dzagoev had to leave the field after picking up a hamstring injury. He raced through a counter-attack before holding the back of his left thigh in the 23rd minute.
Villarreal midfielder Cheryshev replaced Dzagoev for Russia as the hosts continued their good work.
Playing with a strong, disciplined structure with a heavy midfield, Russia controlled the tempo.
Two minutes from time, Saudi Arabia were caught by a counter-attack again and this time it proved costly. Roman Zobnin led the counter-attack for Russia before passing it on to Cheryshev, who employed a left footed shot from the centre of the box to the top left corner to make it 2-0.
After the 2-0 lead, the second half saw less action. While Russia didn't need to up the ante, they managed to contain the Saudis. The Saudi team continued to concede possession to the hosts, unable to push their way up the pitch and create any meaningful opportunities.
At the beginning of the second half, Aleksandr Samedov's right footed shot from outside the box was close, missing out on the top left corner.
Russia got their third goal from Dzyuba, who scored in the 71st minute, one minute after coming as a substitute for Fedor Smolov. Golovin made his second assist of the game as his cross from right saw Dzyuba outjump Saudi captain Osama Hawsawi and head it in.
Russia didn't relent and got their fourth goal in the injury time as Cheryshev got his second of the day. A long ball from the defence was brought down by Golovin before Cheryshev got inside the box before finishing with a chip with his outside of his left foot in the first minute of the second-half injury time.
A couple of minutes later, Golovin fired a sumptuous free-kick to the right post from just outside of the box to make it a overwhelming 5-0 victory.
Earlier Russian President Vladimir Putin declared the FIFA World Cup open after a colourful opening ceremony at the Luzhniki Stadium.
"The love of football unites the world in one team, independent of language or ideology," the Russian president stated during his speech, as reported by Sputnik news agency. FIFA chief Gianni Infantino, two-time FIFA World Cup champion Ronaldo of Brazil and Sweden legend Zlatan Ibrahimovic, Saudi crown prince Mohammed bin Salman and other important personalities attended the opening ceremony.
"I retired from the national team a couple of years ago… It's the best thing that can happen to a player, represent the country in a World Cup. It's a moment of memory, a moment of honour," Ibrahimovic told journalists, reports Sputnik news agency.
The 36-year-old, who currently plays for the US club the Los Angeles Galaxy, has played for a number of European giants, such as Juventus, Barcelona, Milan, Paris Saint-Germain and Manchester United, over the course of his career.
Ibrahimovic is Sweden's all-time top goalscorer, having netted 62 goals in 116 matches before retiring from international football after Euro 2016 in France.
The former Juventus and FC Barcelona striker also felt that Sweden is among the favourites to win the World Cup, along with the likes of Brazil and Argentina.
"They beat some big nations to reach the World Cup, so let's see. Everything is exciting and new. You never know what will happen. It's all about the moment. Whoever is best in the moment is the one that will do well," Ibrahimovic was quoted as saying by the official FIFA website.
"I think Brazil, Spain, Germany, obviously Sweden. Argentina also, even if they don't want to speak about themselves as favourites: they are. I am sorry the US is not in the World Cup because that's my new country where I live, and I would support them also," he added.
At Tottenham, Kane, the two-time English Premier League Golden Boot winner, is the vice captain to Hugo Lloris and has occasionally worn the armband since Wayne Rooney retired from international competition in 2017.
The announcement was made by England manager Gareth Southgate in a live video on Twitter on Tuesday morning.
"Last night, we told the rest of the players that we've named Harry as captain for the World Cup.
"I think it's a fantastic honour for Harry (and) really well deserved. He's got outstanding leadership qualities," Southgate said.
"For me, the key for a captain is that you set the tone for everything that we do every day that we train, the way that we prepare, the professionalism toward the task. He's an exemplary model of that. He's prepared to challenge people, and I think now is a moment in his life where he is prepared and wants to bring that into the team environment.
"He recognises that the success of the team ultimately is how we're all judged as players."
Kane said the selection is "an amazing honour. Obviously, you always dream of playing for England growing up, and to be the captain is a little bit more," he said.
"To be leading the lads out is going to be special, but for me, nothing changes. I'm the same person and same player. It's just about the team. We've just got to do what we can and go as far as we can."
India, who have been clubbed in Group E alongside Bangladesh, Oman, Afghanistan and hosts Qatar, will open their second round campaign of the Asian qualifiers for the 2022 FIFA World Cup against Oman on September 5, followed by a match against Qatar on September 10.
Preliminary squad:
Goalkeepers: Gurpreet Singh Sandhu, Amrinder Singh, Kamaljit Singh, Vishal Kaith.
Defenders: Rahul Bheke, Nishu Kumar, Pritam Kotal, Anas Edathodika, Sandesh Jhingan, Anwar Ali (Jr.), Narender Gahlot, Sarthak Golui, Adil Khan, Salam Ranjan Singh, Subhasish Bose, Jerry Lalrinzuala, Mandar Rao Dessai
Midfielders: Nikhil Poojary, Udanta Singh, Anirudh Thapa, Raynier Fernandes, Vinit Rai, Sahal Abdul Samad, Amarjit Singh, Pronay Halder, Brandon Fernandes, Lallianzuala Chhangte, Halicharan Narzary, Ashique Kuruniyan
Forwards: Balwant Singh, Sunil Chhetri, Jobby Justin, Farukh Choudhary, Manvir Singh