Warriors face Northampton at Franklin's Gardens on the back of four consecutive RaboDirect PRO12 wins, which have taken them to third in the table.
Townsend will again be without fly-half Duncan Weir against the Aviva Premiership leaders but he is adamant Glasgow will face saints with confidence on Sunday.
Townsend said: "This weekend we have the opportunity to achieve something we've never done before, beating a Premiership side in England, and although we know it will be massively tough, we travel with confidence in each other and how we want to play.
"Historically, we've not been fast starters in our pool, and getting results on the board early on is crucial to our firm ambition of qualifying for the knock-out stages.
"It's going to take a very special effort from all 23 players to beat Northampton and establish early momentum in the tournament, but this group certainly has what it takes to achieve that."
Townsend has made three changes from the team that won away at Cardiff Blues on Saturday. Stuart Hogg lines up at full-back, while Ryan Grant and Tim Swinson come into the pack.
Weir, who suffered a knee injury in training last month, faces another six weeks on the sidelines.
Townsend said: "It's clearly frustrating for both Duncan and ourselves that he's missing out on some big games.
"However, with many more important fixtures coming up over the course of the season, it's very important that he gets himself right, and I know he'll be working hard with our medical team to return to the fray in due course."
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