The crowd in Galway were in fine voice as the game kicked off, but it didn't take long for the French side to silence them with a few early scores.
Connacht's first half was a mixed bag, as they went nine points behind before they could respond with a score of their own.
Sébastien Bézy was on target with less than ten minutes gone as he slotted over a penalty, and added another to double his side's advantage shortly afterwards. Florian Fritz kicked over from distance to make it 9-0, and it looked as though last year's Pro 12 Champions might have been letting the bright lights of the big stage get to them a little bit.
Image: ©INPHO/Billy Stickland
However, they exploded into life for a long period in the middle of the half where they began to show the form that had won them the title, and the exciting rugby that made them such a difficult team to play against last season.
After a number of great breaks that bore no fruit, Connacht started a move deep int heir own half that brought the ball through quick hands and over the line.
Bundee Aki made the decisive break through the Toulouse defence, and offloaded to Craig Ronaldson, who was stopped just short of touching down. However, they kept the chance alive and moved it wide, where Niyi Adeolokun was waiting to pounce and cross the whitewash.
Image: ©INPHO/James Crombie
At that stage, it looked as though it was going to be one way traffic for a period, as Connacht's breathless, expansive style began to take its toll on a hugely physical French side. Pat Lam's team showed pace and accuracy with the ball to spread Toulouse all over the pitch, but came away with nothing to show for having played the better rugby for most of the first half.
Toulouse's size advantage began to tell as that first period drew to a close, and they were still able to steamroll their way through the Connacht defence to find two tries in quick succession before the break through Yann David and Jean-Marc Doussain.
A decision to kick to the corner instead of attempting a penalty meant that the home side didn't worry the scoreboard again before the break, as Toulouse went in with a 21-11 advantage.
The opening stages of the second-half were a more cautious affair, as Toulouse were physically dominant but failed to get over the line and add to their advantage. That left the ball firmly in Connacht's court, and despite some early jitters, they accepted the French's invitation to take control of the game.
The man leading the charge was Bundee Aki; breaking with the ball, opening up the defence, getting stuck in at the breakdown to win the ball, there was nothing that he wasn't willing to do in order to drag his side through this game.
Fittingly, he was the man whose try put them level on the scoreboard, but first they needed to narrow the gap, which Tiernan O'Halloran did with aplomb. As Connacht shifted the ball around and went through the phases, looking for a gap, the ball made its way out left, where the Clifden man spotted a gap and fired over the line.
Image: ©INPHO/Billy Stickland
It was up to Aki then to make yet another break a few minutes later, issuing a gigantic handoff on his way over the line for the try that drew them level.
Despite a number of misses in the earlier stages of the game, Carty found his bearings when it mattered most and slotted the ball between the posts to make it 23-21, with a nervous few minutes left on the clock.
Toulouse went in search of something, once again through brute force, but with tired minds and tired legs, Connacht's defence stood strong, going through the phases to see the game out and record a historic victory in the Sportsgrounds in front of an ecstatic home crowd.