Irishman Corr arrived at the far post two minutes from time to tap in Jon-Paul McGovern's slightly overhit cross and end Rovers' impressive unbeaten record away from home.
The former Sheffield Wednesday striker was one of Paul Sturrock's prized assets last season as the Robins clinched promotion from League Two, but has not appeared since May after ongoing problems with a back injury.
Tranmere set their stall out early on and it was obvious manager Ronnie Moore had arrived in the West Country to play for a draw with the hope of maybe snatching a goal on the break.
A strong midfield five passed their way around an indecisive and unstructured Swindon engine room who, with the exception of Lee Peacock, found themselves wanting.
That said the busy Simon Cox was always a willing outlet for the home side and he set up the first definite chance of the match when he cleverly set up Peacock with a nice inside pass, but the former Sheffield Wednesday man's powerful drive was straight at Danny Coyne.
Peacock then forced Coyne into more action with a speculative half-volley from distance which, although looking technically impressive, failed to really trouble the Tranmere goalkeeper.
Despite largely controlling the game Tranmere were failing to really muster any drive in the final third and Gareth Taylor often cast a lonely shadow in the mid-October sunshine, foraging up font on his own.
On 39 minutes however they fashioned their first shot on target when Swindon's Christian Roberts cheaply gave the ball away on the halfway line.
Robbie Stockdale and Steve Jennings kept possession before crossing for Taylor to flick a header on to the onrushing Carl Tremarco, who sent Phil Smith sprawling to his right with a well-directed header.
Billy Paynter missed arguably the best chance of the game a minute before the break as he was denied from eight yards by Coyne when played through by Jerel Ifil.
Despite losing out in the shots on goal stakes it was apparent if Tranmere really wanted to go on and win the game all it would take would be a slight shift in attacking emphasis and the three points would be theirs.
The second half matched the first for unimpressive football as both side toiled in their pursuit of breaking the deadlock.
Full-back Andy Nicholas went close on 73 minutes when he burst into the area only to see his deflected shot clip the outside of Coyne's near post.
Many in the ground thought that the best it was going to get, but Corr's introduction proved significant as he exchanged passes with McGovern on the halfway line before galloping 45 yards into the box and finishing off the matchwinning move.