Wasps beat Bath and Bristol and lost to Exeter in their final game to finish second in Group B.
Hosts Exeter topped the group having won all three of their games, but both teams were assured of reaching the Series Final heading into the final game at Sandy Park.
The Chiefs took an early lead through Joe Simmonds. Wasps fought back through Conor Dolan and Rob Miller, but crucially Max Bodilly grabbed a try just before the hooter as Exeter went into half-time trailing 14-12.
Chiefs skipper Sam Simmonds came to the fore after the break as he scored a try-double - either side of Tom Howe’s score for Wasps - to clinch the win and Group B 26-19.
Last year’s finalists Wasps matched Chief’s six scores in the opening game, as late efforts from Howe, Brendan Macken and Nick De Luca saw them overcome a spirited Bath in a topsy-turvy clash.
Wasps survived playing back-to-back with another win in their second game, but they were made to work for it against a much-improved Bristol who led 14-5 at the break.
Josh Bassett’s double however turned the game in Wasps’ favour before Dolan extended the lead, but Howe was the hero as he denied Elias Caven under the posts with the final play of the game.
Exeter put both themselves and Wasps through with a comprehensive win over rivals Bath in their second game, with captain Simmonds crossing twice early on, before the Chiefs prevailed in the finale.
Wasps 19 (Howe, Dolan, Miller) Exeter Chiefs 26 (Sam Simmonds 2, Joe Simmonds, Bodilly)
Wasps 22 (Bassett 2, Dolan, Hampson) Bristol Rugby 14 (Edwards, penalty)
Wasps 36 (Halai 2, Howe, Cruse, Macken, De Luca) Bath Rugby 21 (Humfrey, Mercer, Atkins)
The Singha Premiership Rugby 7s Series Finals are at the Ricoh Arena on Sunday 7 August. For tickets and details visit Wasps online tickets section.