The Premiership's top two teams threw everything at each other in a compelling match and it was leaders Saracens who survived the second-half sin-binning of flyhalf Owen Farrell to reach the final for the second time in three years.
Wasps, European champions in 2004 and 2007, struck first when winger Christian Wade scorched down the right flank and combined superbly with scrumhalf Dan Robson who scrambled over in the corner.
Saracens dominated possession and made the pressure count as flanker Michael Rhodes charged down a clearing kick by Jimmy Gopperth and pounced on the loose ball to touch down.
Farrell, who had uncharacteristically missed two earlier kicks, knocked over a simple penalty to put Saracens 8-7 ahead at halftime.
Farrell slotted over two penalties after the interval but the England back was sent to the sin-bin for a reckless tackle on Robson and Gopperth reduced the deficit.
Wasps tried to open up the game with their trademark flowing rugby and Wade, who scored six tries against Worcester last week, made a couple of quicksilver runs but the Saracens defence held firm.
Wasps replacement prop Simon McIntyre was shown a yellow card for foul play, Farrell kicked another simple penalty and Saracens moved 14 points ahead with a penalty try after Wasps collapsed a rolling maul.
Still Wasps refused to lie down, however, and replacement hooker Ashley Johnson powered over from close range with two minutes left but it was too late.
English side Leicester play French team Racing Metro in the second semi-final on Sunday.
(Reporting by Ed Osmond; Editing by Rex Gowar)
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