Julien Dupuy's opportunist try less than 50 seconds from full-time handed Leicester a dramatic 20-15 Heineken Cup quarter-final victory over Bath at the Walkers Stadium.
The French scrum-half shaped to feed Sam Vesty for the drop-goal attempt but wheeled away from the base of the Leicester ruck, stole through the fringes and rounded Andrew Higgins to score under the posts.
Leicester will face Toulouse's conquerors Cardiff in the semi-finals at the Millennium Stadium.
The lead changed hands four times in total as Leicester twice fought from behind.
Bath had taken a 10-6 lead shortly after the interval having engineered the one piece of clinical rugby to create a try for Australian replacement Shaune Berne.
Sam Vesty's four penalties nudged the Tigers ahead before Bath pounced on a mistake from Leicester full-back Geordan Murphy and Joe Maddock scored.
But the Tigers again refused to roll over. Vesty drew the scores level with another penalty before Dupuy's piece of magic booked the Tigers a place in the semi-finals.
Even that score was fraught with drama. Dupuy had coughed up possession on the edge of the Leicester 22 and extra-time seemed certain as Lee Mears charged clear.
But Mears' attempted off-load fell into Jordan Crane's hands. Leicester built one final attack - and Dupuy snatched his golden chance.
The conversion was missed and Bath raced to restart the game before the clock ticked over to 80 minutes - but they ran out of time.
The RBS 6 Nations Championship 2015 was not poised to go down as one of the more "vintage" Championships, though there was great anticipation as the action headed into its final day. What transpired was something that nobody could foresee: "The Greatest Day in Rugby's Greatest Championship."