Brady, Court and John Afoa form the front row, while Lewis Stevenson and Dan Tuohy continue their partnership in the second row with captain Johann Muller still sidelined through injury.
Willie Faloon and Robbie Diack get another chance in the back row, where they are joined by stand-in skipper Chris Henry. Mike McComish makes way despite a robust performance in the bonus point win over the Dragons last weekend.
The return of Wallace at inside centre results in a number of positional changes across the back-line. Nevin Spence moves out one to wear the number 13 jersey, with Ian Whitten reverting to the left wing and Stefan Terblanche starting at full-back.
Ulster have plenty of options on the replacements bench, with Paul Marshall, Simon Danielli and Adam D'Arcy all capable of changing the course of the game.
The province's head coach Brian McLaughlin commented: "With Chris (Henry), Tom (Court) and Paddy (Wallace) coming back in it means certain people miss out.
"It shows the strength of the squad that we are building when players like Mike (McComish) and Adam (D'Arcy), who have proved themselves at this level, aren't in the team.
"But that provides challenges for those players and for everyone else in the squad. The competition for places should motivate the players to continue improving."
The Ulster boss is under no illusions about the difficulty of the task his side are facing when fifth plays sixth at the Cardiff Arms Park.
"This is a very important match for us given the position the two teams occupy in the league. There isn't much between us so I suppose you could say it's an eight-pointer.
"But we're playing well at the minute and if we play like we have done over the past few weeks, we have a good chance of coming back with the result."
Indeed, Ulster have produced some excellent performances in recent times and have now registered six bonus point wins in their last eight games.
McLaughlin says confidence is a key factor in the recent purple patch his side have enjoyed, adding: "We're a confident side now and we know we can beat anyone on our day.
"There is a good atmosphere amongst the squad and the management and we feel we're moving forward.
"We will continue to push towards our goals and a win on Friday would be another step forward in terms of qualification for the PRO12 play-offs."
ULSTER (v Cardiff Blues): Stefan Terblanche; Craig Gilroy, Nevin Spence, Paddy Wallace, Ian Whitten; Ian Humphreys, Ruan Pienaar; Tom Court, Nigel Brady, John Afoa, Lewis Stevenson, Dan Tuohy, Chris Henry (capt), Willie Faloon, Robbie Diack.
Replacements: Andi Kyriacou, Paddy McAllister, Adam Macklin, Tim Barker, Mike McComish, Paul Marshall, Simon Danielli, Adam D'Arcy.