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.
Leinster were forced into a late change with Schmidt not willing to risk Jonathan Sexton, who suffered a knock to his left ankle in the win over Glasgow Warriors.
Ian Madigan came in for his first Heineken Cup start, distributing well early on as the wind-backed hosts enjoyed the early possession.
Purposeful runs from front rowers Richardt Strauss and Healy pinpointed the chinks in Montpellier's defence, and soon after a short burst from O'Brien - aided by Damian Browne - saw him muscle over from close range.
McFadden added the conversion and a penalty to take the province into double figures, before Kearney sliced through off first-phase ball.
From a midfield scrum, Isaac Boss and Gordon D'Arcy combined to send the full-back through the defensive line and, although Paul Bosch hauled him down, Kearney stretched out his left arm to get the touchdown.
McFadden made it a seven-pointer but good ball retention from the visitors' bulky forwards got them close to a first try, big Mamuka Gorgodze being thwarted by Leo Cullen and O'Brien.
Leinster held them up again through a series of five-metre scrums and assaults on their line, albeit with Browne being sin-binned for side entry at a ruck.
It was a punishing period for the home forwards but the French outfit just could not break them down, with a steal from tournament debutant Jamie Hagan lifting the siege.
Montpellier captain Fulgence Ouedraogo infringed at a central ruck as Leinster finished the first half back in the visitors' half. McFadden rifled over the resulting penalty.
A sparkling run from Isa Nacewa helped Leinster lay down an early marker in the second half.
D'Arcy went close to scoring in the right corner before Healy powered over on a muscular drive with support from Rhys Ruddock and replacement Mike Ross.
Kearney was inches away from scoring his second try, his attempt from a quick tap being snuffed out by the well-placed Alex Tulou.
Substitutions diluted the intensity slightly until a final spurt from both sides saw Montpellier get off the mark and Leinster fail to muster a bonus-point score, with McFadden lacking the support required to finish off the best of the chances.
Two late penalties from Olly Barkley helped
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.
With both sides having no hope of progressing in this tournament The Rec crowd may have hoped to see an enterprising tussle, but they were instead treating to stodgy, error-strewn fare during the first 40 minutes.
Weir had booted the Warriors into a third-minute lead with his first penalty, but it was his error that gifted Biggs the opening score.
The outside-half looked to shift the ball on while under pressure, and his loose pass was gathered in by Biggs who raced in from halfway for a try converted by Barkley.
Scrum-half Chris Cusiter's chargedown of opposite number Chris Cook quickly put Bath on the back foot and forced a second penalty for Weir to convert, but the Scottish side were already showing signs of struggling to handle the home pack.
The Warriors front row of Jon Welsh, Pat McCarthur and Ed Kalman were under constant pressure at scrum time, conceding a string of penalties, while Bath's driving maul was proving an effective weapon.
Barkley extended the home side's lead to four points in the 17th minute with his second penalty, after John Barclay was harshly penalised for not rolling away, but a lack of accuracy at crucial moments meant Bath did not take advantage of their forward edge.
Countless promising attacking positions went begging, either from crooked line-out throws or clumsy handling, and their half-time lead would have been just a single point had Weir being able to land a difficult long-range penalty effort just before the interval.
But Bath finally made the dominance of their pack tell four minutes into the second stanza as a well-controlled, trundling maul worked its way over from fully 25 yards, with Skirving emerging from the heap of bodies to claim the score. Barkley added the extras with the help of an upright.
There were injury worries for Scotland coach Andy Robinson as prop Ed Kalman joined lock Ali Kellock in being forced but, against the odds, Glasgow almost found an instant reply after referee Christophe Berdos somehow missed McCarthur's crooked throw at a line-out on halfway.
Barclay cut through the Bath midfield and smart handling sent wing Colin Shaw over, only for the final pass to be ruled forward.
But the Warriors did strike back after the most cohesive period of attacking play in the entire contest as they stretched Bath one way and then the other to create a weight of numbers that allowed replacement Scott Wight to give Seymour an easy finish.
Wight, on for Weir, knocked over the conversion to trim the lead to four and Glasgow's fightback was given added impetus when Cook was sin-binned for killing the ball.
And the Warriors second try was not long in coming as centre Stuart Hogg streaked down the right to second back-rower Harley over to put Glasgow a point to the good with 17 minutes to play.
But having fought so valiantly to get back in the game the Warriors were caught trying to play their way out of their own half, and Barkley punished them with another penalty to put Bath back ahead, before adding another three-pointer in the dying minutes.