Exeter had already sealed top place and rested international stars like Stuart Hogg, Henry Slade, Jack Nowell and Jonny Gray.
Wasps’s win guaranteed second spot and a home semi-final next weekend, although the identity of their opponents is unknown following Premiership Rugby's postponement of the clash between Sale Sharks and Worcester Warriors until Wednesday after 16 Sharks players tested positive for coronavirus.
If that game takes place - it is subject to stringent retesting - and Sale win with a bonus point, then they will travel to Wasps.
Jacob Umaga, Dan Robson, Jimmy Gopperth and Josh Bassett all scored tries before substitute Ben Vellacott collected a second-half double.
Gopperth finished with 19 points after also kicking four conversions and two penalties, with Rob Miller converting Vellacott's second try and prop Danny Southworth touching down for Exeter.
Wasps' eighth win from nine starts since the Premiership resumed in August was their biggest league victory over Exeter.
Bristol Bears also secured a semi-final place by scoring five tries in a 36-7 victory over London Irish.
Semi Radradra, Ben Earl, Harry Thacker and Will Capon crossed for the visitors, who were also awarded a penalty try. Max Malins added the rest of Bristol's points with a penalty and three conversions.
Irish could only respond with a second-half try from Ollie Hassell-Collins which Paddy Jackson converted.
Leading 17-3 entering the final quarter, Bath looked set for a first win in north London since 2010 that would have guaranteed a last-four spot.
Saracens appeared to have been undone by an impressive start by Bath, who crossed through Beno Obano and Ben Spencer.
But their final game in the Premiership following relegation because of breaching salary cap regulations ended with a bang rather than a whimper.
A penalty try and a 73rd-minute touch down by Tim Swinson, which was converted in treacherous conditions by Manu Vunipola, kept Bath hanging on.
Harlequins provided a fitting farewell to former England captain Chris Robshaw with a 32-26 bonus-point victory over Leicester at Welford Road.
Robshaw, 34, led his team out for his 300th and last appearance and played the full match as tries from Alex Dombrandt, Joe Marchant (two) and James Lang, along with 12 points by fly-half Brett Herron, saw Quins home.
Leicester replied through Tom Youngs, Nemani Nadolu and Mike Scott, plus three penalties and a conversion from George Ford.
Gloucester were given a 20-0 win over Northampton after Saints had forfeited the game.
Northampton, who met Sale on Tuesday, called the game off as a number of their players have to self-isolate and Gloucester finish seventh in the table.
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