Fly-half Toby Flood kicked three penalties as 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.
While Flood missed only one of his four shots at goal, Toulouse kickers Lionel Beauxis and Luke McAlister crucially botched five attempts between them and Leicester prevailed 9-5 to top Pool Two.
"It was a game when it was almost easier to play without the ball," Tigers rugby director Cockerill told Sky Sports 2. "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.
"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 for that."
Toulouse wing Yann Huget scored the only try in an encounter dominated by the incessant wintry weather, with Leicester ultimately joining their Aviva Premiership colleagues Harlequins and Saracens as quarter-finalists alongside Toulon, Munster, Ulster, Clermont Auvergne and Montpellier.
It was the first time since 2007 that four-time European champions Toulouse failed to progress from their group as Leicester thwarted them on the back of Flood's goalkicking accuracy and mighty contributions from forward warriors like Louis Deacon, Tom Youngs and Julian Salvi.
Skipper Deacon said: "We had to dig deep towards the end - fair play to the lads. It was absolutely freezing out there. We needed it, we were at home and we don't lose many at home. The crowd was absolutely amazing, they backed us all the way, and we probably wanted it more in the end."
Toulouse had a late chance to deny Leicester a famous win, but they messed up a lineout just five metres from Tigers' line under pressure from the mighty defensive efforts of Deacon and his second-row partner Geoff Parling.
And Flood, who was still shivering during his post-match interview, said: "It is a difficult draw, but we've got through. It wasn't ideal out there today. It was a real dog-fight, but we dogged it out. There was plenty of grit and grind."
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