The Altrad Stadium battle will go down in Scotstoun folklore as the Pro12 high-flyers claimed their second win on French soil in Europe’s premier competition.
Finn Russell produced a faultless kicking display, with his five penalties from five attempts leading his side to glory and sending a statement to Scotland coach Vern Cotter.
The Warriors had to sustain spells of heavy pressure from the Top 14 side, but they held on to make it a two-horse race in Pool 4.
Nicolas Mas crashed over to claim a losing bonus point late on but Glasgow march into back-to-back matches with Toulouse on top of their group.
Montpellier operate on a budget of more than ¤20 million but the Scots always looked the more likely to take the spoils back to Scotland.
Russell calmed Warriors’ nerves after just two minutes. Townsend’s men went on the offensive from the first whistle and their early pressure told when Montpellier blind-side Kelian Galletier crashed into an airborne Tim Swinson.
The 22-year-old stand-off landed the confidence-boosting kick to give the visitors an early 3-0 lead.
Rene Ranger can count himself lucky for not seeing yellow just two minutes later when his flailing arm stopped Tommy Seymour from streaking downfield.
The flying wing intercepted a pass destined for the Kiwi but was stopped in his tracks by the infringement, and Stuart Hogg struck the upright with the long-range penalty.
But Russell resumed kicking duties after the French side were once again guilty of getting on the wrong side of referee JP Doyle. They went offside as Glasgow threatened and the No.10 drilled over his second of the day to stretch the lead.
The hosts finally sprung to life after 15 minutes and won a penalty on their first visit to Warriors’ territory. Scrum-half Benoit Paillaugue struck it sweetly to close the gape.
Russell was given the chance to prove his Scotland credentials once more after Montpellier continued to offend. It was No.8 Alex Tolou’s turn to go off his feet at a ruck and Russell re-established the six-point advantage.
And Glasgow marched back downfield thanks to their free-flowing outside backs. Russell combined with Alex Dunbar after fielding a long boot downfield before the ball found it’s way to Mark Bennett, who crafted a perfectly weighted grubber kick downfield.
France full-back Benjamin Fall collected, but could not get past a wall of white and blue chasers, and was forced over his own line for a five-metre scrum.
Henry Pyrgos brought Seymour into play off the base of the scrum and he collided with home second-row Sitaleki Timani. He came off worse and was stretchered off after a long period of treatment.
Bennett bashed away at the French line from the resulting scrum and Euan Murray almost furrowed his way to the line. But the Montpellier defence repelled the attack and forced a turnover.
Paillaugue reignited the kicking duel with his second penalty of the afternoon after the Scots entered a maul from the side for a half-time score of 9-6.
Scotland stand-off Duncan Weir was introduced moments after half-time and his first contribution was to hook a 22-metre restart straight into touch after Paillaugue failed with a penalty.
The lax strike sparked a shift in the match’s momentum.
Murray was penalised for bringing down a scrum and instead of levelling the scoreline, the French went for the jugular and kicked to the corner.
Glasgow showed their mettle by out-muscling their opponents from the resulting lineout drive. But they were on the back foot moments later after Murray suffered more scrum woes, Montpellier won the contest against the head and pounded the advantage line once more through Akapusi Qera and their duo of Fijian wingers.
But it was Russell to the rescue as he collected a Montpellier knock-on and fired his side back downfield.
Russell made it four from four on 60 minutes to reinstate the six-point gap. And he booted his side to only their second win in French soil in Europe’s premier competition after Enzo Selponi deliberately knocked down a Glasgow pass.