Josh Bassett's late try sent Wasps into their first Aviva Premiership final for nine years as they edged out Leicester Tigers 21-20 at the Ricoh Arena.
Jimmy Gopperth and Willie Le Roux sent Bassett into the corner with two minutes to play, to end the ever-dogged Leicester's stubborn resistance.
Wasps will face Exeter - who saw off Saracens with a late try of their own - in next weekend's Premiership final, returning to the league's Twickenham trophy showdown for the first time since 2008.
But boss Dai Young's side may have to face the obdurate Chiefs without star man Kurtley Beale after the Australia flyer limped off with a leg problem.
The Wallabies star will do everything to recover for the final though, for one more Wasps match before heading back Down Under.
Beale grabbed Wasps' first score as they led early on but Leicester drew level at 13-13 courtesy of Peter Betham's score.
Telusa Veainu's second-half try for the Tigers left Wasps throwing everything at a madcap recovery, with Bassett just finding time to turn the tide.
Leicester captain Tom Youngs was unable to cap a testing few weeks by guiding his side to the final but was lauded by both sets of supporters, all aware his wife Tiffany has been diagnosed with terminal cancer.
The Tigers' bravery and granite grit so nearly trumped Wasps' fluent back play, but in the end the hosts had it - but only just.
Young had ordered Wasps' marquee players to earn their hefty wages in knockout rugby, and his two star turns quickly set about that task.
Wasps quickly turned a bludgeoning catch-and-drive into a rapier finish, Beale and Le Roux conjuring a sumptuous one-two for the game's first try.
Springbok flyer Le Roux's fine floated inside ball returned the favour after Beale had set him loose, and the Wallabies full-back slid home for the score.
Gopperth added the conversion to his second-minute penalty, leaving Wasps 10-0 to the good inside 10 minutes.
Two quickfire Burns penalties and a riposte from the tee from Gopperth put the hosts 13-6 ahead in the second quarter, but finally the Tigers' backline purred.
Burns' superlative miss-two cut-pass proved enough to catch Christian Wade in no-man's land and send wing Betham in at the left corner.
Danny Cipriani took a heavy hit from Dom Barrow at a ruck in the build-up to that score, but television match official (TMO) David Grashoff ruled out any foul play.
Burns' conversion locked the scores at 13-13, and so it stayed when Gopperth struck the right-hand post off the tee.
The Kiwi marksman slotted his third penalty of the half shortly afterwards however, to hand Wasps a 16-13 lead at the break.
Wasps started the second half brightly, but were rocked by losing star man Beale to a suspected left leg injury.
Leicester scented blood, and pounced when cutting out Ashley Johnson's optimistic looped pass.
Brendon O'Connor powered close on a fine tight line and when the Tigers whipped the ball wide, Wasps simply ran out of cover. Veainu cantered home, with Burns' conversion edging the visitors into a 20-16 lead.
Youngs then departed to a standing ovation from both sets of fans, the supporters all fully respectful of his family's battles.
Wasps' harem-scarem wide play stretched Leicester to the brink throughout a pulsating final quarter.
The hosts botched two lineouts in the Leicester 22, wasting a hard-won scrum penalty.
But just when they feared losing their chance to steal victory, Wasps pilfered possession and sneaked home as Le Roux and Gopperth combined to send replacement wing Bassett into the corner.
Gopperth slipped on impact to strike the conversion wide, setting up a nervy final minute. But Wasps ground down the time, sealing victory, safe passage to the Premiership final - and raucous celebrations at a rocking Ricoh Arena.