Wasps goal-kicker Jeremy Staunton kicked 17 points, but Wasps needed a late intercept try to winger Ayoola Erinle to seal the win. Fly-half Staunton missed with an early dropped-goal attempt, but was on target from the sideline in the 10th minute and again from near the halfway line a minute later as the London side dominated the opening exchanges.
The Tigers regathered and produced a couple of forays into enemy territory, but it was the 30th minute before the scorers were troubled, and it was that man Staunton banging over his third penalty goal for a 9-0 lead. The first try came in the 33rd minute when Tigers winger Tom Varndell regathered an Austin Healey chip to score out wide.
Staunton recovered from a heavy knock to kick his fourth goal, and Wasps took a deserved 12-5 lead into the halftime break. Scrum-half Healey inspired the Tigers' second try when his break gave centre Leon Lloyd the space to dot down, but Wasps retained the lead when Andy Goode's conversion attempt rebound off an upright.
The London club continued to hammer at the Tigers' try-line but had to settle for a fifth Staunton goal as they went into the final quarter with a five-point cushion. The Tigers desperately tried to score the match-winning try in the final 10 minutes, but a loose ball was snapped up by Erinle, who scampered 80 metres to put his side into the Cup final.
The Tigers scored a late consolation try through centre Dan Hipkiss.
Tries - T Varndell, L Lloyd, D Hipkiss; Con - A Goode
Try - A Erinle; Pens - J Staunton 5; Con - J Staunton
Halftime: Wasps 12-5
Referee: Nigel Owens (Wales)