And while qualification for the Heineken Cup quarter-finals may be beyond them, the result means they could continue their European adventure in the Challenge Cup if they can topple Toulon next weekend at Scotstoun Stadium.
Toulon, the reigning Heineken Cup champions, have lost just one game in Pool 2 in this season's campaign and Townsend believes his side have nothing to lose against the French outfit.
"We knew that if we were able to win here and other teams were to lose then there could be a chance of getting into the Challenge Cup if we were to pull off a win next week," said Townsend.
"It was great to get the win. We didn't play that well, especially in the second-half but we defended really well throughout the 80 minutes and in Europe the club have not won in England before, so that was great.
"We've got Toulon coming to Glasgow next week and nothing to lose. Hopefully we can play like we did in the second-half against them over in France. That was some of the best rugby we've played this year.
"We know how difficult it's going to be, they'll be coming to Glasgow looking for a win to get a home quarter-final and they've got great depth and great quality throughout their squad but we believe we can play better than we did [against Exeter].
"We've had a game now to blow away the cobwebs and we'll focus well on doing all we can to win next week. It'll probably be the biggest game we've ever played at Scotstoun."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up to our newsletter for regular updates on the RaboDirect PRO12
63x46.png){kind=logo}