Tigers came back from 16-8 down early in the second-half to win 34-19 and secure a crucial try bonus point in victory.
The five-point haul sets up a huge clash with Ulster Rugby at Welford Road on Saturday (6pm) with the winners topping Pool 5 and securing a home quarter-final. It also guarantees Richard Cockerill’s men at least one of the two best runners-up spots and a place in the last eight.
"We got what we set out to achieve from the game and that was maximum points,” said Tait. “At half time we were in a bit of a hole but it's a mark of this team that we've been in that position a few times this year and we've managed to dig ourselves out of it.
"That's testament to the group. We've got some really experienced guys in there and players who put us in the right parts of the field, certainly in the second half.
"By our own standards, the first half wasn't really good enough. The last 30 minutes were a better reflection of how we wanted to play.
"A lot of teams get caught out coming down here - it's a difficult place to play. We knew that Treviso are a very physical team and they would make it difficult. Our standards will have to be a lot higher against Ulster."