Deciding to bat, Karthik's 48-ball 86 and Sharma's unbeaten 50-ball 74 powered Mumbai Indians to an imposing 209 for five before the hosts produced a disciplined bowling effort to restrict Delhi Daredevils to 165 for nine in their alloted 20 overs at the Wankhede Stadium.
Australian opener David Warner waged a lonely battle for Delhi with a 37-ball 61 but none of the other batsmen showed intent to grind it out and bind time at the wicket.
The pressure of mounting run rate weighed heavily on Delhi batsmen as they kept on losing wickets at regular intervals.
Defending the target, Mumbai bowlers kept a tight leash over Delhi's scoring rate to earn their second successive win in the tournament after losing their first match against Royal Challengers Bangalore.
Mitchell Johnson, Kieron Pollard and Pragyan Ojha picked up two wickets apiece while Lasith Malinga and Harbhajan Singh too accounted for a wicket each for Mumbai.
Tuesday's result meant that Delhi slumped to their third successive defeat with the absence of key overseas players and an injured Virender Sehwag hurting the team's chances badly.
Delhi were off to a poor start as opener Unmukt Chand yet again failed to deliver the goods for the visitors and went for a first-ball duck for the second time in this IPL season.
Mumbai skipper Ricky Ponting took a stunning catch with one hand while diving full length to his right at extra cover to dismiss Unmukt off Harbhajan Singh.
Delhi skipper Mahela Jayawardena too fell cheaply as he was caught by wicketkeeper Karthik off Mitchell Johnson for three, leaving Delhi stuttering at 13 for two inside three overs.
Even though wickets kept tumbling at the other end, Warner was hardly bothered as he went about his business in style and kept the run rate well in check with his occassional strikes.
Delhi reached their 50 in the seventh over with Warner hitting left-arm spinner Ojha for a huge six over deep mid-wicket boundary. Warner kept on punishing the Mumbai bowlers as he hit a six and a four off Pollard in the 10th over to bring up his fifty.
Warner found an ably ally in Manprit Juneja (49) as both kept the scoreboard ticking along at a fair pace.
Both forged an 82-run partnership for the third wicket in just 48 deliveries before Johnson returned back for his second spell to dismiss Warner, who was looking solid during his innings of 61 off 37 balls, laced with five fours and four sixes.
The departure of Warner spelt doom for Delhi franchise as they lost three wickets in quick succession.
Jeevan Mendis (0) was caught by Pollard off his own bowling while Irfan Pathan was caught by Johnson off Ojha at deep midwicket for 10. Kedhar Jadhav's departure further compunded the misery for Delhi as they were left tottering at 132 for six in 16 overs.
Delhi kept on losing wickets at regular intervals as the visitors succumbed under the pressure of mounting run rate.
Juneja's 40-ball 49 was decorated with four fours and he was run out by Rishi Dhawan in the 18th over.
Earlier, Karthik and Sharma treated the opposition bowlers with disdain as both helped Mumbai recover from two early jolts.
Karthik continued his rich vein of form as he hit 14 fours and two sixes in his aggressive knock while Sharma too played his role to perfection.
Sharma's chanceless knock was laced with 4 fours and five towering hits beyond the boundary line, which included three sixes off the last over bowled by pacer Ashish Nehra.
Ambati Rayudu too played a little cameo, hitting an eight-ball 24 laced with two fours and an equal number of sixes.
Mumbai got off to a worst possible start as the two batting stalwarts of the game, Ponting and Sachin Tendulkar, departed within a few balls of each other with just one run on board.
Pathan first got rid of Ponting (0) on the final ball of the first over before Mumbai got off the mark. In the next over, Tendulkar got run out, giving Delhi edge in the early overs.
Karthik and Sharma then joined hands in the middle and both of them started the repair job.
After watching on few deliveries, Karthik upped his tempo and exploded in the sixth over, hitting Nehra for one six and two fours to accumulate 16 runs off the over. He smashed pacer Umesh Yadav for three fours in his second over to bring up his fifty in just 30 balls with the help of nine fours and one six.
Karthik went about his business in style and forged a 132-run stand with Sharma as the duo sent the bowlers on a leather hunt.
South African pacer, Morne Morkel broke the stand when he had Karthik caught at extra cover by Mendis.
Next man-in, Pollard did not last long as he departed for 13, caught by Shahbaz Nadeem at extra cover off Nehra.
Rayudu then joined forces with Sharma and accumulated 22 runs of Pathan's last over and innings' 19th before being caught by Nehra off his own bowling. Sharma then hit three sixes off Nehra's final four deliveries to post the highest IPL total at the stadium.