Simone Favaro, Grayson Hart, Peter Horne, Stuart Hogg, Jonny Gray and James Malcolm each scored a try apiece, meaning Angelo Esposito's Treviso try was in vain as the visitors ran out 38-16 victors.
Townsend's men play Zebre rugby on Friday night and he told the Warriors website his team were spurred on by the visiting fans.
He said: "The first part of the Italian Job is done and we know it'll be tough next week against Zebre but we were pleased to get the bonus-point in Treviso and we'll move forward with confidence.
"When we were warming up we saw a few fans but when we got into the stand there were loads.
"That shows what the players mean to the supporters and also how the club has evolved. To play Treviso away from home and have a few hundred fans over with us really helps.
"There was a lot of effort that went into that second-half performance. The way we started that 40 minutes showed what the players are capable of as there was quick support to the ball carrier.
"We had to be strong to clear the defensive threats as well which we did.
"To score six tries was pleasing and that will happen when there are open conditions and you play multi-phase rugby with spaces starting to open up.
"Players like Stuart Hogg found mismatches in defence and he scored a cracking try. Grayson Hart also showed great initiative with his score."
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