Fly-half Ruaridh Jackson notched 22 points, including a try, with Sean Maitland, Niko Matawalu, Mark Bennett, Stuart Hogg and John Barclay also on the scoresheet which helped the Warriors to an eighth win in nine games.
Next up is a trip to fifth-placed Scarlets on April 12, and with the Scottish side nine points ahead of the Parc y Scarlets outfit Townsend knows a win would secure a top four place.
But he also wants victories against Ospreys and Connacht in the Warriors' final two fixtures to seal a fantastic campaign.
"The players have a real belief about what they are doing," said Townsend.
"If we win one or two we should be top four. If we win them all that will keep us in the top two. The play-offs was the aim at the start of the season.
"We need to really prepare well. Scarlets play differently to a number of teams and have a very strong defence so it'll be extremely tough.
"But I believe with the way the players are playing and the effort they are going to put in during training over the next ten days when they come back from their holidays, we'll have a good chance of winning down there."
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