Best returns to captain the side at hooker, with Payne named at outside centre and Bowe selected on the right wing.
Bowe is joined in the back three by Louis Ludik and the Guinness PRO12's leading try scorer, Craig Gilroy.
Darren Cave partners Payne in the centre with Paddy Jackson and Ruan Pienaar continuing in the halfbacks.
Up front, Callum Black and Wiehahn Herbst start either side of Best with Dan Tuohy and Franco van der Merwe selected in the second row.
Roger Wilson returns to the side at Number 8 with Iain Henderson picked at blindside and Chris Henry at openside in what will be his first start since recovering from heart surgery.
Forwards Rob Herring, Andy Warwick, Bronson Ross, Robbie Diack and Clive Ross join backs Paul Marshall, Ian Humphreys and Stuart McCloskey on the replacements bench.
The game is live on Sky Sports and BBC Radio Ulster.
Ulster team & replacements to play Connacht, Guinness PRO12, Sportsground, Saturday 11th April (14:40 kick off): (15-9): L Ludik; T Bowe, J Payne, D Cave, C Gilroy, P Jackson, R Pienaar; (1-8): C Black, R Best (C), W Herbst, D Tuohy, F Van der Merwe, I Henderson, C Henry, R Wilson;
Replacements (16-23): R Herring, A Warwick, B Ross, R Diack, C Ross, P Marshall, I Humphreys, S McCloskey.