Struggling Rovers gave an excellent account of themselves at a gale-lashed Carrow Road, only to be undone by a controversial 60th-minute penalty awarded when John Welsh was adjudged to have handled Adam Drury's fierce drive.
Welsh had his back turned when the ball struck him, but referee Darren Deadman decided it was deliberate handball and Wes Hoolahan converted from the spot.
Tranmere missed the chance to take the lead minutes earlier when Chris Shuker hit the post after a smart one-two with Michael Ricketts.
A late goal from Gary Doherty added an extra touch of gloss for the Canaries, who maintained their drive towards the top two of League One.
Doherty slid home from close range after Hoolahan had set up an easy chance, to leave the home fans celebrating and Rovers feeling hard done by.