In blustery conditions, Sean O'Brien's ninth-minute try settled any early nerves and man of the match Rob Kearney used his speed and strength to nab his fourth try of the pool stages.
Montpellier had no points to show for a long spell in the home 22, trailing 20-0 at the break with Fergus McFadden booting the rest of Leinster's points.
Joe Schmidt's men went further ahead with a try from Cian Healy and, in a scrappy final half-hour, Martin Bustos Moyano kicked a penalty for the visitors.
The result completed an unbeaten run through the six rounds for the Pool Three winners, who are guaranteed to be one of the top seeds in the knockout phase.
In the other Pool Three game, two late penalties from Olly Barkley helped Bath overcome a brave Glasgow fightback and end a disappointing campaign with a 23-18 victory at The Rec.
Bath had held a 10-6 lead after a turgid opening half thanks to a Tom Biggs try and five points from centre Barkley's boot, fly-half Duncan Weir replying with two penalties for the visitors.
The second half mercifully proved to be a far more entertaining affair. Ben Skirving's converted try extended Bath's lead before Glasgow turned the game on its head as wing Tommy Seymour and flanker Rob Harley crossed.
But Barkley had the last word as he claimed a personal haul of 13 points to give the hosts just a second win in nine games, and end Glasgow's lingering hopes of an Amlin Challenge Cup quarter-final spot.
Ulster will be away in the quarter-finals after losing 19-15 at Clermont Auvergne.
The teams were level at 6-6 at the interval but a try from Ti'i Paulo in the second half saw the French side top Pool Four at the expense of their visitors.
Leicester's disappointing European campaign came to an end with a
comfortable but far from convincing 33-6 win over a battling Aironi at Welford Road.
Forwards Thomas Waldrom and Ed Slater were the star performers for the Tigers, who led only 9-6 at half time before second-half tries from Thomas Waldrom, Ben Woods, Geordan Murphy and George Ford saw them pull clear.
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