Cronin, who missed the Leinster game as part of the IRFU Player Welfare Programme, replaces Adrian Flavin at hooker.
In a reshuffled back-line, Carr takes over from Brian Tuohy on the left wing. Ian Keatley has been moved to full-back, with Troy Nathan now on the right wing and Eoin Griffin, Connacht's lone try scorer against Leinster, joining stand-in captain Keith Matthews at centre.
Meanwhile, back rower Mike McComish has recovered from flu and will start Thursday's game on the replacements bench.
Regular skipper John Muldoon heads the province's injury list, with Gavin Duffy (knee), Ronan Loughney (hamstring) and Ezra Taylor (hand) also currently sidelined.
Speaking earlier this week, head coach Eric Elwood said: "We have had to rest guys this week. There is a lot of them broken up after the weekend.
"Michael Swift, Mike McCarthy, Jamie Hagan, Brian Tuohy, Johnny O'Connor and Keith Matthews all missed training - they are just battered.
"We were disappointed (to lose to Leinster) at the weekend. We did a lot of good things in the first 20 minutes but we didn't take out chances.
"But to be fair, I thought Eoin McKeon had a terrific game and I thought Andrew Browne was outstanding.
"With his prominence in attack and in defence, Brownie has really stepped up to the plate in the last couple of weeks and I actually paid tribute to him today. He was outstanding.
"I also thought Eoin Griffin did really well on the wing as well and it is great to see. They are three of our own young lads so that is positive, because we have always said that if they are good enough they will get their opportunity."
CONNACHT (v Newport Gwent Dragons): Ian Keatley; Troy Nathan, Eoin Griffin, Keith Matthews (capt), Fionn Carr; Miah Nikora, Cillian Willis; Brett Wilkinson, Sean Cronin, Jamie Hagan, Michael Swift, Mike McCarthy, Andrew Browne, Johnny O'Connor, Eoin McKeon.
Replacements: Adrian Flavin, Rodney Ah You, Dylan Rogers, Bernie Upton, Mike McComish, Frank Murphy, Niva Ta'auso, Brian Tuohy.