Connacht boss Pat Lam said his team always believed they could pull off a shock result against Toulouse despite their poor form this season.
Toulouse suffered a 16-14 defeat at home by Connacht on Sunday, who had won just two matches all season prior to the Pool Three Heineken Cup clash.
But the victory at Stade Ernest Wallon took the Irish province to within one point of the pool's pacesetters - held by Toulouse and Saracens - and kept alive their hopes of reaching the quarter-finals.
"We had a lot of belief coming to this game," said Lam.
"Although we are at the bottom of the (PRO12) table this year, every single game we played we could have won.
"We have a team with no superstars, we missed so many opportunities throughout the season, but we still came here confident. We just had to make sure that everyone did their job.
"There was a lot of trust out there - I'm very proud of that tonight. Last week against Edinburgh we should have won comfortably, but they scored three tries in the last five minutes.
"At the time it hurt, but it might be the best thing that could have happened to us. We had a look at our shape and it was badly wrong, we spent a lot of time at the start of the week getting back to our defensive shape.
"When we had that today we were able to put pressure on Toulouse. We're very happy that the boys were able to do that, because then we could play as a team.
"At half-time, we mainly talked about ourselves, about playing our game. I said, 'they're giving us opportunities, we just need to recognise them'. The homework we did on them paid off - every time we attacked, we had opportunities.
"The try they scored before half-time happened because someone left the gate open, it was just a bad call, a system error. We're alive, and now we have to go and do the same in our own backyard.
"This will be a big effort, because we'll face a hurting Toulouse team. They're going to be written off and told how bad they are. They'll come to us fired up."