Piutau suffered delayed onset concussion after last week's win over Ospreys while van der Merwe sustained an ankle ligament injury in the game.
Tommy Bowe provides a boost with the Ireland wing making his first start in six months following a knee injury.
Connacht have made six changes from the side that beat Edinburgh last Saturday.
Cian Kelleher will start on the left wing in place of the injured Matt Healy.
Peter Robb and Kieran Marmion are both sidelined with injuries so inside centre Craig Ronaldson will make his first appearance of the season following his return from long-term injury while Caolin Blade starts at scrum-half.
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Up front, hooker Dave Heffernan has been handed his first start of the campaign in the absence of the injured Tom McCartney.
With Denis Buckley ruled out, returning Ireland international Finlay Bealham comes in at loosehead.
Andrew Browne, who returns from injury, is handed his first appearance of the season and partners Ultan Dillane in the second row.
Ulster scrum-half Ruan Pienaar is rested by director of rugby Les Kiss while Callum Black comes into the front row.
Robbie Diack and Peter Browne form a new second-row partnership and Clive Ross replaces Sean Reidy at openside flanker.
Defending champions Connacht, who have only earned one win over Ulster in 20 attempts, are ninth in the standings.
Connacht: T O'Halloran; N Adeolokun, B Aki, C Ronaldson, C Kelleher; J Carty, C Blade; F Bealham, D Heffernan, C Carey, U Dillane, A Browne, E McKeon, J Heenan, J Muldoon (capt).
Replacements: S Delahunt, R Loughney, JP Cooney, L Stevenson, J Connolly, S Kerins, S O'Leary, S Ili.
Ulster: J Payne (capt); T Bowe, L Ludik, D Cave, C Gilroy; P Jackson, P Marshall; C Black, R Best, R Ah You, R Diack, P Browne, I Henderson, C Ross, R Wilson.
Replacements: R Herring, A Warwick, R Kane, K Treadwell, S Reidy, D Shanahan, B Herron, R Lyttle.
Pro12 leaders Ulster will be without injured pair Charles Piutau and Franco van der Merwe for the derby against Connacht in Galway on Friday night.