The talented Australian, who ran up a tally of 32 points in the westerners' last European outing in Galway, struck nine successes with his right boot from ten attempts, to tally up his season's points to 141 in 12 games.
The 23-year-old also chipped in with an early try to start the rout. Warwick converted before returning fly-half Eric Elwood drew the cover for former Ireland Under 21 Conor McPhillips to touch down on 20 minutes.
Hooker Bernard Jackman's bulldozing 23rd minute run saw Ted Robinson dash over after a lapse from former Scotland international Gregor Townsend for the French side. The visitors' only points came from the boot of full-back Frederic Benazech on the half hour. Michael Bradley's outfit were unrelenting and ran up a 26-3 half time advantage.
Matt Mostyn won a 45-metre kicking chase with winger Laurent Arbo to touch down on 29 minutes for Connacht's fourth, and his third in three games.
Second half efforts from McPhillips, flanker John Muldoon and substitute Conor O'Loughlin - spliced with three Warwick penalties - saw Connacht deservedly over the half-century.
Montpellier's woes were compounded in the final stages as substitute Bertrand Guilloux was sin-binned for repeat infringing.
Second round, first leg:CONNACHT 56 Montpellier 3, The SportsgroundScorers: Connacht: Tries: Warwick, McPhillips 2, Robinson, Mostyn, Muldoon, O'Loughlin; Cons: Warwick 6; Pens: Warwick 3 Montpellier: Pen: Benazech
(15) Matt Mostyn
Replacements used: Conor O'Loughlin for Mostyn (51 mins), Dan McFarland for Hogan (62), John Fogarty for Jackman, Pieter Myburgh for Short (both 63), Peter Bracken for Knoop (68), Brendan O'Connor for Muldoon (69), Mike Walls for Keane (78).