Wilkinson takes over from Ronan Loughney in the front row, Swift will start in the second row and Muldoon gets the nod at number 8.
It will be Ireland international Muldoon's first start since returning from a broken arm. He last started for Connacht against Harlequins in the Amlin Challenge Cup before Christmas. The selected pack boasts 842 Connacht caps.
Swift is making his return from a hand injury which saw him miss the westerners' last two matches. He joins former Junior All Black Bernie Upton at lock, with the versatile Mike McCarthy moving to blindside flanker.
Johnny O'Connor continues to captain the side at openside flanker for what is Connacht's penultimate interprovincial clash of the season.
The back-line remains largely unchanged from last weekend's home defeat to the Cardiff Blues, with Frank Murphy partnering Ian Keatley at half-back.
Keatley is the the second top points scorer in this season's Magners League, just 19 points behind the Ospreys' Dan Biggar. The Munster-bound out-half has landed 72 kicks at goal as well as scoring two tries during the league run.
New Zealand Barbarian Troy Nathan and former Samoan Under-21 Niva Ta'auso make up the centre pairing again, and Fionn Carr and homegrown talent Eoin Griffin link up with Ireland International Gavin Duffy in the back-three.
Speaking ahead of Friday's match, head coach Eric Elwood said: "We know it is going to be difficult. Ravenhill is an intimidating venue and Ulster are playing good rugby - they are physical in the exchanges, compete at the breakdown and play direct rugby and we will have to match them.
"After their two defeats (to Northampton and Leinster) they will see this an ideal opportunity to get back to winning ways.
"Traditionally we do not have a good record there, a record that goes back over years, but that is irrelevant for most of our players.
"This is the second year in-a-row that we've been forced to play Ulster away in the second last match of the season and it is tough.
"Historically Ulster have seen us as the team they must overcome to secure a Heineken Cup place, and a derby fixture is always highly competitive, so we know we have to up our performance and up our game."
CONNACHT (v Ulster): Gavin Duffy; Eoin Griffin, Niva Ta'auso, Troy Nathan, Fionn Carr; Ian Keatley, Frank Murphy; Brett Wilkinson, Sean Cronin, Jamie Hagan, Michael Swift, Bernie Upton, Mike McCarthy, Johnny O'Connor (capt), John Muldoon.
Replacements: Adrian Flavin, Ronan Loughney, Rodney Ah You, Andrew Browne, Mike McComish, Cillian Willis, Miah Nikora, Tiernan O'Halloran.