The striker’s header opened the scoring after 18 minutes before Ash Taylor equalised for Rovers just before the break.
But Garner, North End’s leading scorer this season, took his tally to 16 in all competitions with a 52nd-minute effort.
Preston, who have lost only twice in the league since October, drew first blood when Garner headed a Craig Davies cross back across goal.
Despite Preston’s dominance Tranmere levelled in the last minute of the first half when Taylor smashed in from close range after good work from Ryan Lowe.
Rovers started the second half brightly and hit the crossbar through a Jason Koumas free-kick.
But shortly afterwards it was Preston who were celebrating when Garner slotted past Owain Fon Williams after a through ball from Scott Wiseman.
Preston began to dominate and had chances to put the game beyond Tranmere through Wiseman, Davies and Scott Laird, but they still held on to extend their unbeaten run in the league to four games.