This was the second time in the tournament that Ireland managed to chase down target in excess of 300.
Stirling`s 177-run partnership -- their highest in the tournament -- with skipper William Porterfield laid the foundation for the chase as the Irish dished out a clinical display with the bat to romp home in 47.4 overs after electing to field first.
Stirling struck a breezy 72-ball 101, which was studded with 14 boundaries and two sixes, while Porterfield`s 68 came off 93 balls, and included 10 fours.
Niall O`Brien struck a quickfire 57 not out with seven fours, while Gary Wilson took just 21 balls to score 27 (2x4, 2x6) in a 46-run fourth-wicket stand after the departure of the opening duo.
The junior of the O`Brien brothers, Kevin, who struck a century in their shock win over England in another 300-plus chase, provided the finishing touches with some big hits as he remained unbeaten on 15 from nine balls (2x6).
In the morning, Ryan ten Doeschate hit a delightful 106 from 108 balls (13x4, 1x6) for his second World Cup century, while skipper Peter Borren extended fine support with an 82-ball 84 (10x4) as their 121-run partnership helped the Netherlands recover from a sloppy start to post a challenging 306.
Ten Doeschate, who has been roped in by the Kolkata Knight Riders for the upcoming Indian Premier League, made a statement in front of his `home` crowd as he was cheered for his every boundary and six.
But the Dutch showed their inexperience at this level with four run-outs in succession with addition of just one run in the last over, which meant that they side were bundled out for 306 in a dramatic fashion.
Ireland were never really in trouble while chasing, despite Porterfield`s shaky start to his innings.
Stirling, on the other hand, was at his belligerent best taking the attack to the Dutch camp as their bowlers and fielders had a forgettable outing.
The Netherlands bowling lacked sting and, barring a maiden each from ten Doeschate and Adeel Raja, who sparkled in their first spells, the Dutch bowlers failed to make an impact.
Stirling began his innings with a six, and the all-rounder was at his aggressive best against Bernard Loots, who was drafted into the side in place of Tom de Grooth.
Stirling hit three fours and a six off Loots, who conceded 29 runs from two overs, as the opener cruised to his half-century off 25 balls.
Having been dropped on one and 41, Porterfield also gained in confidence, as he completed his fifty in 70 balls.
The introduction of spin broke the match-winning partnership but by that time, Ireland were already sitting pretty, and the middle-order capitalised on the great start to finish the job.
Ireland, who had famous wins over Pakistan and Bangladesh, which helped them make the Super Eights stage in the 2007 World Cup, stunned England in an astonishing 328-run chase earlier in the tournament.
The Irish stretched the West Indies and India before going down, but their quarters hopes ended after defeat to South Africa.
Roped in by the Kolkata Knight Riders, 21-year-old ten Doeschate had yesterday promised a century at the Eden to set the tone for his stint here, and he did not disappoint the sparse crowd.
After being reduced to 53/3 inside 11 overs, ten Doeschate led the recovery with a 60-run partnership with Wesley Barresi (44), before putting them in a strong position with an entertaining 121-run stand with the skipper.
Put into bat, the Netherlands had a shaky start against their familiar foes, with Boyd Rankin and Trent Johnston giving the opening duo of Eric Szwarczynski and Wesley Baressi tough time at the crease.
Barresi was dropped on zero at second slip, but the opener retired hurt after being hit on the back of his neck.
Ireland bowlers struggled without left-arm spinner George Dockrell, who was taken off the attack after dislocating his right shoulder.
In the fourth ball of his fourth over, the 18-year-old dived full length to his right to save a single from ten Doeschate only to hurt himself. The promising spinner finished with seven wickets, including the prized scalp of Sachin Tendulkar, in the tournament.
Meanwhile, the Dutch opener returned after the dismissal of Alexei Kervezee in the 11th over, and plundered the Irish attack for runs during his crucial stand with ten Doeschate.
Atse Buurman hit a quickfire 26 from 30 balls (4x4) to help the Dutch go past the 300-mark as the Irish bowlers struggled with their rhythm.
But four consecutive run-outs in the final four balls meant that the Netherlands ended their innings on 306, which, in the end, proved too easy for Ireland.