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The Ospreys - whose two wins in this season's competition are the only ones from 10 games Welsh sides have played in - scored the one try of the game, through man of the match Eli Walker, against a Toulouse side that totally under-performed.
Leicester went top of the pool after they eked out a come from behind 14-13 win over Treviso in Italy.
The English side, who travel to Ospreys in the next round of matches in January, lead Toulouse by a point with two games remaining while Ospreys are five points adrift of the pool leaders.
Leicester host Toulouse in what should be a thrilling final pool game.
Ospreys - who had never beaten Toulouse in three previous meetings - got off to the better start as they needed to do in a match they had to win to stay in contention for the knockout stage.
Fly-half Dan Biggar knocked over an early penalty and then a well-taken drop goal to give them a 6-0 lead and the hosts received another boost in 25th minute when Toulouse's Argentinian lock Patricio Albacete was sin-binned for over zealous use of the boot.
However, Jean-Marc Doussain - normally a scrum-half but having to slot in at fly-half in place of the injured Luke McAlister - reduced the deficit with a penalty shortly before the half hour mark.
Biggar restored the six point advantage with another penalty but Doussain dropped a goal on the stroke of half-time to make it only 9-6 to the hosts.
Doussain, though, missed a kickeable penalty in the 56th minute which would have drawn them level and four minutes later the visitors woeful display got worse when experienced flanker Jean Bouilhou was sin-binned for a high tackle on the outstanding 20-year-old wing Eli Walker.
Walker made them pay double for that as he was released on the left wing and evaded a dreadful attempt at a tackle by opposite number Yoann Huget to touch down - Biggar missed the conversion to leave it at 17-6 and hard as Toulouse tried they were unable to make any inroads.
Leicester got off to a bright start against Treviso, scoring a superb try which went from one end of the pitch to the other, wing Adam Thompstone touching down.
However, the hosts drew level in the 28th minute as Irish referee Alain Rolland awarded Treviso a penalty try after the scrum colapsed eight metres out.
The Italians then added a penalty to lead 10-7 at the break and extended their lead with a penalty by Alberto di Bernardo but late in the match Leicester were awarded a late penalty try which they converted to edge the game 14-13.
