Keatley kicked three penalties and converted Carr's first half try to extend Connacht's impressive unbeaten home run, which stretches back to September, and dent the Dragons' play-off hopes.
Paul Turner was missing Wales squad members Luke Charteris and Danny Lydiate from his side. They are on international duty this week while he was also unable to call upon the services injured trio of Adam Jones, Lewis Evans and James Harris.
Connacht were largely dominant and the Dragons were restricted to just a single penalty from 20-year-old out-half Jason Tovey.
It was clear from the off that Keatley, who is two years older than his opposite number, would have the better platform to work off as the Connacht forwards were very effective at set piece time, with lock Mike McCarthy stealing two Dragons lineouts.
That hard graft up front saw Keatley convert two penalty goals after 9 and 15 minutes and Michael Bradley's men moved 13-0 ahead at the midpoint of the half, completing a terrific breakaway try.
Scrum half Conor O'Loughlin used turnover ball to make a break and kick through for Liam Bibo to chase. He gathered well and found his fellow winger Carr with a lofted pass, and Connacht's top try scorer of the current campaign did the rest, outpacing the cover to score close to the posts.Keatley added the extras onto Carr's twelfth try in 16 outings this season.
The Dragons, with Toby Faletau making his first start and Andrew Coombs debuting as a replacement in the second half, showed signs of life with some strong running from centre Matthews Watkins.
But their wide men were kept out of the game as Connacht kept play tight. Tovey landed a penalty to cut the gap to 13-3 for half-time, after Tom Willis and his Dragons forwards were stopped five metres out.
However, the Dragons were off colour once again during a rather listless second half.
With John Muldoon and George Naoupu carrying well, Connacht built through the phases impressively, setting up an early penalty kick for Keatley which he sent through the posts.
The Ireland international missed two further place-kicks, and while the Dragons almost hit back with a try - Bibo produced a brilliant hit on Watkins to force a turnover - and ended the game camped on the home line, Connacht held firm to hand the Welsh side their first defeat in five matches.