Connacht were outscored two tries to one but Kieran Marmion's second-half effort combined with 11 points from the boot of fly-half Dan Parks - who successfully kicked two penalties, a conversion and a drop goal - saw them claim a huge scalp.
Four-time champions Toulouse notched tries in either half through Jean-Pascal Barraque and Thierry Dusautoir but they could not find a way to break down the Connacht defence again in the closing stages as they slumped to a rare home defeat in Europe.
Munster moved to the top of Heineken Cup Pool 6 as they swept past a weakened Perpignan team 36-8 at Thomond Park.
The injury-hit French club are noted for their poor away form with only one win on the road since March, and Munster built a 22-0 half-time lead without finding top gear.
A breakaway score from man-of-the-match Keith Earls supplemented tries from forwards Sean Dougall and David Kilcoyne as Rob Penney's men coasted clear.
Perpignan captain James Hook responded with a penalty and Munster had to be patient for their bonus point reward - a 66th minute penalty try sealed their five-point return before James Couglan and Joffrey Michel exchanged late efforts.
Wing Martyn Thomas scored tries in both halves as Gloucester beat Edinburgh 23-12 in their Heineken Cup clash at Murrayfield.
The home side had taken an early lead in the Scottish capital when Greig Tonks danced in to score after six minutes.
But the lead lasted just four minutes before Rob Cook levelled for the visitors.
Thomas then touched down twice to give Nigel Davies side an 18-point lead before David Denton scored a converted try to give the scoreline a more respectable look for Edinburgh.
The victory moves Gloucester on to eight points in Pool 6, two behind leaders Munster, with Perpignan on six points and Edinburgh on four.
Miles Benjamin scored twice in two minutes as Leicester claimed a spirited 41-32 win over Montpellier in Sunday's Heineken Cup clash at Welford Road.
The 25-year-old repaid Leicester's faith following more than a year out through a serious neck injury with two first-half scores after Vereniki Goneva had given the Tigers the lead in the fifth minute.
Flanker Jamie Gibson sealed the bonus point for Leicester with his second-half score as Toby Flood kicked 18 points for the Tigers.
Montpellier had looked out of the match at 24-3 down, but they rallied through tries by Mamuka Gorgodze, Timoci Nagusa and two for Pierre Berard as they claimed a try bonus point of their own.