The win ensures a semi-final clash against either Newcastle Falcons or Castres later in the month with the prize a place in the European final.
Director of Rugby Mike Ruddock was pleased with the way his side had edged the clash and kept the cup campaign on track.
"There is a big prize at the end of this and we are delighted to make the semi-finals," he said.
"We produced a really good first half and with the ball in hand we looked great. We played with purpose and skill, combining it with good decision making and accuracy."
The game was delayed for ten minutes after a medical emergency in the North Stand but when play did get underway it was Warriors that made a dream start with centre Dale Rasmussen making a break in midfield and Miles Benjamin racing up on his shoulder to touch down under the posts. Fly half Shane Drahm, who earlier boomed a huge 70 metre clearance, slotted the conversion to put Warriors in the driving seat.
French side Montpellier hit back with some passion and style as France international flanker Fulgence Ouedraogo scored in the corner and Federico Todeschini adding the conversion to draw the two sides level.
Warriors were hit by the departure of lock Craig Gillies who was replaced by Will Bowley for blood after only seven minutes and Montpellier were looking threatening when they had the ball in hand.
The game was flowing from end to end and Worcester went back in front after 20 minutes after another initial burst from Rasmussen. The ball was spun through hands and skipper Pat Sanderson made the final pass to Gear who strode over for his sixth try in Europe this season. Drahm added the extra points for a 14-7 lead.
Benjamin was almost in for a second try of the afternoon after a steepling kick from Drahm but as the French full back dithered it was just knocked on by the young winger before he gathered and looked to race over.
Worcester should have had a third try of the afternoon when more pressure saw fly half Drahm dance through a gap only to be tackled short with Gear screaming for a pass wide right. Desperate Montpellier defence saw them stray offside and Worcester opted for the scrum.
The French side shunted play back but only denied the inevitable as Powell picked up and fed Drahm who, after picking up a difficult pass, released Sam Tuitupou who needed no second invitation to run in for the third try of the afternoon.
Montpellier again looked to reply with scrum half Sebastien Buada picking up at the breakdown and racing through a gap before his grubber kick almost found wing Sebastien Stoica. The wing, though, was not to be denied and another break from Ouedraogo saw Stoica race in with the score converted.
The high scoring game continued with Gear the next to benefit from the opening running approach as he burst past two men from close range to score. Drahm continued his impressive display with an accurate kick.
The tries continued to flow with Tuitupou bursting past men to come close to scoring again. Powell was quick to pick up the ball and feed Gillies who on the right wing dived over. Drahm did the rest to stretch the lead to 33-12 at the break.
Montpellier braved an early second half storm from Warriors and hit back with a passage of sustained pressure on the Worcester line.
It paid off on the hour when hooker Fabien Rofes crashed over for a third try for the visitors after Pat Sanderson was sinbinned. The numerical advantage also counted as South African Warren Britz raced over to set up a grandstand finale with the lead cut to seven.
Montpellier refused to lie down and continued to run from deep as the clock ticked down but Warriors held firm and Drahm scored a late penalty to ensure victory and place in the last four.
03m Benjamin t Drahm c 7-0
07m Ouedraogo t Todeschini c 7-7
20m Gear t Drahm c 14-7
26m Tuitupou t 19-7
32m Stoica t 19-12
35m Gear t Drahm c 26-12
38m Gillies t Drahm c 33-12
60m Rofes t Todeschini c 33-19
68m Britz t Todeschini c 33-26
72m Drahm p 36-26
Warriors: 01 Tony Windo, 02 Aleki Lutui, 03 Tevita Taumoepeau (Ruwers 76), 04 Greg Rawlinson (Bowley 56), 05 Craig Gillies (Bowley 7-16), 06 Drew Hickey, 07 Pat Sanderson, 08 Kai Horstmann, 09 Matt Powell (Arr 76), 10 Shane Drahm (Carlisle 76), 11 Miles Benjamin, 12 Sam Tuitupou, 13 Dale Rasmussen, 14 Rico Gear, 15 Thinus Delport
Replacements: 16 Matt Mullan, 17 Shaun Ruwers, 18 Will Bowley, 19 Gavin Quinnell, 20 Joe Carlisle, 21 Jonny Arr, 22 Chris Pennell