The Tigers' win made it a fine weekend for English rugby as they became the third Premiership team to reach the quarter-finals. The first time that has been achieved since 2009.
Fly-half Toby Flood kicked three penalties as the Tigers held on, despite Flood's late sin-binning, to secure a quarter-final place and send Toulouse into this season's Amlin Challenge Cup knockout phase.
"It was a game when it was almost easier to play without the ball," he said. "They missed some kicks at goal, and, to be fair to Toby, he kicked that one just before half-time to give us a nine-point cushion.
"The effort at the end, those last two minutes with the crowd on their feet, they are magic moments.
"This team wants to make its own history. This club has a rich history and there is a lot said about players in other eras. Today, this team knocked Toulouse out of the Heineken Cup.
"We won a really tough pool, the players should be congratulated for that and we should get some credit."
Leicester take on Toulon in France in the last eight, with the winner facing Saracens or Ulster away. Saracens edged Ulster out of the home quarter-final spots with a five-try win over Edinburgh in poor conditions that saw them top Pool 1.
Director of rugby Mark McCall, who now faces a rematch with his old club, paid tribute to his side's patience after England winger Chris Ashton crossed for two tries in the 40-7 rout.
"The key was being patient and to keep our composure, but also to control the game enough through position and with that the opportunities would come and then we would put them away," McCall said.
In Pool 2, Treviso claimed a first win of this European season in their final game, edging the Ospreys out by 17-14.
On Saturday, Clermont secured second place in the standings to book a quarter-final date with Montpellier by winning their sixth pool game in a row. Vern Cotter's side scored 29 unanswered points at Parc y Scarlets, with tries from Napolioni Nalaga, Morgan Parra, Benson Stanley and Aurelien Rougerie securing the bonus point against the hapless Scarlets.
Montpellier booked their place as the top-ranked second place team with a strong display in their 23-3 victory over Toulon.