The three-time champions inflicted revenge on Marcelo Loffreda's men after Leicester's tight 14-9 win in the reverse fixture at Welford Road last weekend.
Leinster's shock loss to Edinburgh at Murrayfield on Saturday turned Pool Six into a two-horse race.
But tries by Clement Poitrenaud and Vincent Clerc secured a vital win to put Toulouse five points clear and deny the Tigers of a losing bonus point which leaves them needing a minor miracle to reach the quarter-finals.
England star Corry said: "It's now out of our hands and we'll have to look at other results.
"It's very disappointing and we knew we had to win here to keep control of our own destiny.
"But we've failed to do so and as a consequence, we need to rely on others.
"It's not ideal but we've let ourselves down by not getting anything out of our two away games.
"But I know we've got character in our side and we need to show we can win back-to-back games."
Byron Kelleher insists it was payback time as Toulouse crushed Leicester in the Heineken Cup at Le Stadium.
The former New Zealand scrum-half came on as a replacement in the second half and reckoned his team-mates were ready to avenge last weekend's loss in the east midlands by delivering a much-improved performance.
Kelleher said: "We let ourselves down last week and we knew it was payback time.
"I thought we definitely had more power up front and in the back line than Leicester and I'm really happy with our progress this season.
"But it's more important at this stage of the season that we have cohesion in our play and build friendships within the team and squad.
"And we're doing a great job out there of playing for each other.
"Whether we can win the competition is a long way off because we've got a lot of games to play.
"We have to keep producing back-to-back performances and showing a consistency which all top teams do.
"But we've got a great depth in this team and we'll be a force this season."