After their colleagues had departed following breezy fifties on a good M Chinnaswamy Stadium track, Iyer (128 not out) struck his fourth ODI ton before Rahul (102) exploded as the duo lit up the stage on the Hindu festival of Diwali to get India to 410-4.
Requiring a record World Cup chase to win, the bottom-placed Dutch side got good starts from Max O'Dowd (30), Colin Ackermann (35), Sybrand Engelbrecht (45) and Teja Nidamanuru (54) but they never threatened and were dismissed for 250 in 47.5 overs.
Mohammed Siraj (2-29) overcame a throat injury suffered in a dropped catch to dazzle alongside Kuldeep Yadav (2-41), Jasprit Bumrah (2-33) and Ravindra Jadeja (2-49) to secure victory for India, who face New Zealand in the semi-finals on Wednesday.
"Honestly, since we started the tournament it was always about taking one game at a time and playing that game well," said Indian captain Rohit Sharma.
"That's what everyone did. We're very pleased with how we played in these nine games. We've been clinical from game one. That's because different individuals have stepped up at different points.
"This is a good sign for a team when everybody wants to take responsibility and get the job done."
HIGHEST FOURTH-WICKET STAND
Iyer reached his century in 84 balls and finished with 10 fours and five sixes while Rahul needed only 62 balls for his ton, getting there with two huge sixes in the last over that took India past 400.
The duo forged a 208-run partnership - the highest fourth-wicket stand in World Cups - as India scored 126 runs in their final 10 overs to post the third total above 400 in the event.
"I hurt my arm on 95 so I had to settle down and take a bit of time," said man of the match Iyer.
"My last few innings have given me a lot of confidence. It wasn't an easy wicket to start on, it was playing tacky, a bit two-paced so I knew I had to make the most of a good start."
India put the Netherlands to the sword after winning the toss and opting to bat as Rohit (61) and Shubman Gill (51) hit boundaries at will to give them a superb platform with 91 runs in the powerplay.
Gill was severe on the bowlers with three fours and four sixes, but the world's top-ranked batsman found the man in the deep while taking on a short one from Paul van Meekeren after reaching his 12th half-century.
The Netherlands chipped away and were rewarded when Bas de Leede had Rohit caught at wide long-on, but Kohli (51) and Iyer took India past 200 runs in the 29th over with a 71-run stand.
Kohli delighted the crowd with a wide array of shots after a shaky start to his quest to reach 50 ODI tons and eclipse Sachin Tendulkar's record, but Roelof van der Merwe briefly silenced fans by breaking his stumps with a flatter one.
"India showed pure class with the bat. I thought we bowled well in periods," Dutch skipper Scott Edwards said. "They soaked up the pressure. They're going to be a hard side to beat in the rest of the tournament.
"As for ourselves, we're a young side still and it's about growth for us."
