There was little in the way of quality in a fast-paced encounter at Prenton Park. The managerless hosts made a lot of the early running but Stockport keeper Owain fon Williams made good saves to deny Gareth Edds and Terry Gornell.
Baker and Greg Tansey then fired wide for County while Vincent brought a diving stop from Daniels before the break.
The visitors looked the more assured side as the match wore on and Baker was only inches from breaking the deadlock on the hour. And soon after County did take the lead, Baker beating replacement keeper Joe Collister with his spot-kick after Daniels had seen red.
Craig Curran and Ian Thomas-Moore went close for Tranmere late on but Stockport held on for a valuable win that lifts them to 13th in the League One table.