Leicester will travel to Toulon in the Heineken Cup quarter-finals after they beat Toulouse to win Pool Two as the French giants' goal-kickers fell apart.
Toby Flood gave Leicester a 9-0 half-time lead as the visitors missed three penalties at a snowy Welford Road.
A Mathew Tait error allowed Yoann Huget to reduce the lead to 9-5 with a try.
Who plays who in last eight?
Harlequins v Munster
Clermont v Montpellier
Toulon v Leicester
Saracens v Ulster
But Luke McAlister could not convert and he then missed Toulouse's fourth penalty as two-time champions Leicester edged into the last eight.
Lionel Beauxis and McAlister missed a brace of penalties apiece, hitting the woodwork once each, but there was still a nerve-wracking finish as the hosts lost Flood to the sin-bin.
Toulouse camped in the Tigers' half, but their kickers' inability to find the target means the French club's bid for a record fifth Heineken Cup is over for another year.
Leicester had removed 50 tonnes of snow from the pitch in the 48 hours leading up to the game but more fell throughout the match and contributed to an error-strewn encounter.
Toulouse fielded a massive pack and Leicester's cause was not helped when 6ft 6in blind-side Steve Mafi pulled a hamstring early in the game.
Flood's accuracy from the tee kept Leicester's Heineken Cup hopes alive
But Leicester could have taken the lead when Adam Thompstone came from the opposite wing to arc through the outside centre channel and feed Morris.
The Irish winger blasted through the tackle of Vincent Clerc but lost the ball as he tried to ground it at full stretch, and that was as close as the Tigers were to come to a try - not that they will care.
The temperature in the east Midlands may have been freezing but out on the pitch it was boiling hot and a series of flash points kept things simmering throughout the first half, with Flood landing three penalties out of four to give Tigers a 9-0 interval lead.
Beauxis missed Toulouse's first two attempts, hitting the woodwork with the second, before McAlister took over and hit the opposite post as the visitors enjoyed a purple patch midway through the half but failed to come away with any points.
They thought they had scored a try when the mighty Louis Picamoles got his tree trunk thighs working to power over from a quick free-kick, but the television match official could not establish whether the France number eight had grounded the ball and Leicester escaped.
The second half started with the erratic Beauxis adding to his collection of missed chances as he pushed a drop-goal wide but Leicester full-back Tait then handed them a try.
He failed to gather a swirling kick from McAlister as it plummeted out of the snow and although Tait grabbed it at the second attempt he was tackled as he tried to clear and the tumbling Huget dribbled the ball over the line and dotted down for the score.
But McAlister failed to convert and when he then missed a penalty, the anguish on the face of Toulouse coach Guy Noves told its own story.
Leicester suffered a major scare as Flood was sin-binned for a deliberate knock-on as he chased back after having a kick charged down.
But the Tigers' fighting spirit shone through as they resisted Toulouse's best efforts and Geoff Parling stole a late attacking line-out to ensure it is the Tigers who will travel to the Mediterranean coast in the last eight to face Jonny Wilkinson's Toulon.
View from the dressing room
Leicester boss Richard Cockerill:
"It was a game when it was almost easier to play without the ball. 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 for that."
Tait; Morris, Tuilagi, Allen, Thompstone; Flood, B Youngs; Ayerza, T Youngs, Cole, L. Deacon, Parling, Mafi, Salvi, Waldrom.
Crane for Mafi (16), Ford for Tait (68), Hamilton for Thompstone (66), Castrogiovanni for Cole (63).
Medard for Poitrenaud (69), Burgess for Doussain (72), Kakovin for Steenkamp (65), Botha for Tolofua (58), Montes for Johnston (65), Millo-Chluski for Maestri (57), Nyanga for Lamboley (45).
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