The return fixture in the south of France comes a week after Tigers scored a 41-32 bonus-point victory over their Pool 5 rivals at Welford Road.
Tries from Miles Benjamin (2) and Vereniki Goneva got Tigers off to a dream start in the home leg. But, even after a bonus-point try from Jamie Gibson in the second half, French visitors Montpellier were within six points from four tries of their own before a late Ryan Lamb drop goal finally settled the outcome.
Director of rugby Richard Cockerill said: “We had that purple patch of 10 minutes where we could do nothing wrong and it was probably as well as we’ve played for a long time. But then got a bit giddy and didn’t take some of the other opportunities we created.
“In the end it was a great spectacle and it was great to get the points out of the game.
“Montpellier are a very good side. We said through the week that if we gave them loose ball they would score and they certainly did that. They could have had more, so could we, there were probably four or five tries left out there from both teams.
“We know it will be tough next week and we have to get ourselves ready.
“They are at home, they will be hurting from today and they showed how dangerous they can be.
“They will be looking forward to it. It’ll be a big physical battle. We have got to get our mentality right, play well and cut out the errors.”