Leicester boss Richard Cockerill hailed the win away in Montpellier as "massive" in order to keep the pressure on Ulster.
A three-point gap remains at the top of Pool 5 between the Irish and English sides after four rounds, with Ulster yet to visit Welford Road.
Heroics from Vereniki Goneva and Ryan Lamb snatched victory away from a much-changed Montpellier outfit on Sunday, as Leicester won away in France for the first time since 2006.
"You give Montpellier a few opportunities and they will score and then you're chasing your tail," said Cockerill.
"At 14-8 we could have been happy to take the bonus point and not risk losing it but credit to the players, they kept playing and manufacturing opportunities to score tries even if we didn't necessarily take them.
"But this was what we needed in the competition, those four points to keep the pressure on Ulster.
"This is massive for us, with another massive game in Treviso to come. We can't take anything for granted but we want to get the win there and then bring Ulster at Welford Road for a grandstand finish.
"It's a massive win and potentially the defining moment that can get you out of a pool.
"This puts us in good position to finish top of the group, and maybe get a home quarter-final.
"But there's still a long way to go, we can't take Treviso lightly but it's still in our hands.
"I'm delighted for the players, it's their victory. We hadn't won in France since 2006, this group of players have made a little bit of history for themselves."
Singling out loosehead prop Marcos Ayerza for a sublime touch in the build-up to Goneva's clincher, Cockerill added that the Tigers coped well despite the loss of playmakers Toby Flood and Dan Bowden.
"We played pretty well and had a few good opportunities to score. Miles Benjamin was a whisker away and we could have scored a few more so we did enough to win the game," added Cockerill.
"It is what Leicester do well, they keep doing what they do, they keep playing. Even today with Toby (Flood) going off and Daniel Bowden going off, the lads just kept playing, knowing that opportunities would come.
"Fair play to Marcos Ayerza after 79 minutes he showed what makes the difference between being good and very good. And to Niki Goneva for getting up again to get close to the sticks for a better conversion."