The defending English champions scored 26 unanswered points after the interval to book their place in next Saturday's showpiece encounter and rescue their dream of winning the title for a third successive year.
Lawrence Dallaglio's side have never lost a match in three seasons of Premiership play-off history and in Leicester they will meet the club with whom they have shared control of domestic rugby for the last seven years.
Tom Rees, Josh Lewsey, Ayoola Erinle and Simon Shaw crossed as Wasps edged the try-count 4-3 with five of the touchdowns arriving in a hugely-entertaining first half which Sale deserved to finish ahead.
Tries from Sebastien Chabal, Jason White and Mark Cueto helped them to a 22-17 interval lead but Wasps upped the tempo for the second half, taking a stranglehold on the match which Sale could not break.
They were assisted by the flawless kicking of Mark van Gisbergen, who finished with 20 points, and a raft of stand-out individual performances as the club's big guns began firing after the break.
Sale's cause was not helped by the loss of Charlie Hodgson who had hobbled off after a heavy collision on the half-hour mark, especially as the England fly-half's kicking sights were clearly well adjusted.
It was Hodgson who drew first blood with an early penalty, but Wasps created a glorious opportunity to snatch the lead in the seventh minute when a series of forward drives close to the line created a one-man overlap.
Possession was swiftly fed left to Lewsey who found van Gisbergen with a long pass that missed out Erinle, but the Kiwi dropped the ball with a simple run-in beckoning.
Wasps' next attack was rewarded by a King drop-goal but Warren Gatland's side suffered a setback at the ensuing 12th-minute restart when England second row Shaw spilt Hodgson's hanging kick.
The ball bounced out of his arms and was scooped up by White who found Chabal at close to full tilt, giving van Gisbergen little chance of stopping the rampaging Frenchman. Hodgson added the extras.
Paul Sackey pulled off a try-saving tackle on Steve Hanley in the left corner but the Wasps winger then nearly cost his team a try when he chose to go it alone instead of feeding Tom Voyce in support.
Luckily, Wasps kept the move going with Voyce and Joe Worsley almost crossing before a big sufficient overlap had been created for the ball to be shipped right where openside Rees strolled over.
Lewsey added a stunning solo effort in the 25th minute when he came up with the ball after a Sale attack had broken down and dashed from inside his own 22 to the Sharks' line, slipping past Jason Robinson on the way.
Van Gisbergen added both conversions before Sale slashed the deficit to two points in the 32nd minute when a powerful run from Robert Todd broke several tackles with the centre able to supply the scoring pass to White who barged over.
Richard Wigglesworth – on for the injured Hodgson – was off target with the conversion but a canny cross-field kick from the substitute saw Sale edge into the lead with one minute of the half left, Cueto collecting his punt to the far side and finishing.
Van Gisbergen slotted a penalty shortly after the interval and Wasps then regained the lead after a powerful rolling maul took them within a couple of yards of Sale's line with Erinle finishing the move by crashing over.
Van Gisbergen converted and added his second penalty a heartbeat later before Wasps were forced to repel a series of attacks just five metres from their whitewash, pushing the Sharks back and breaking out from their own 22.
Rees was stretchered off after a melee of players appeared to land on his leg, which was positioned awkwardly, but the incident did not put Wasps off their stride with van Gisbergen slotting two more penalties to complete the scoring.
For London Wasps:Tries: Rees, Lewsey, Erinle, Shaw Cons: Van Gisbergen 3Pens: Van Gisbergen 5Drop: King
For Sale Sharks:Tries: Chabal, White, Cueto Cons: Hodgson, Wigglesworth Pen: Hodgson