Leicester won the first penalty shoot-out in Heineken Cup history to book a Murrayfield showdown with Leinster on May 23.
The Tigers, European champions in 2001 and 2002, kept alive hopes of a third title thanks to number eight Jordan Crane’s 22-metre kick which concluded a bizarre end to a contest which went to extra-time.
Leicester won the penalty shoot-out 7-6, Crane striking gold after Blues’ Wales and Lions flanker Martyn Williams missed.
Both teams were reduced to taking shots at goal from in front of the posts and Cardiff had the advantage when Leicester wing Johne Murphy missed his team’s fourth kick.
However, Blues wing Tom James, whose late try had taken the game into extra-time at 26-26, fired his kick wide, allowing the Tigers to live again via sudden death.
It was a cruel way to end a pulsating contest, especially when it seemed as though a remarkable Blues fightback would reap a spectacular reward.
The Welsh side looked down and out, trailing 26-12 with just six minutes of normal time remaining.
But converted tries by Wales internationals Jamie Roberts and James - which rounded off an electrifying 80-metre move - looked to have halted Leicester’s Murrayfield march.
It took the game into extra-time and Leicester only had themselves to blame, having a player - flanker Craig Newby and then full-back Geordan Murphy - in the sin-bin for each score.
But after a scoreless extra 20 minutes, Williams proved the villain and Leicester took the glory.
It keeps them on course for a third European and domestic double as they face Bath in the Guinness Premiership play-offs in six days’ time.
At one stage Leicester looked as though they could afford marksman Julien Dupuy to miss his first three kicks at goal, such was their dominance for much of the contest in front of a 44,000-strong crowd.
But Dupuy came up trumps by landing his next six, giving him a 16-point haul to complement superbly-worked tries for wing Scott Hamilton and Murphy.
Ben Blair and Leigh Halfpenny each kicked two penalties for the Blues, but Toulouse’s quarter-final conquerors failed to score after trailing 13-12 at half-time until their late two-try burst.
Blair nervelessly added both touchline conversions, yet it was Leicester who ultimately prevailed amid dramatic scenes.