Hume found the net against his former club five minutes after Jake Cassidy looked to have salvaged a draw for the League One leaders after 87 minutes, pouncing to cancel out Billy Paynter's opener in a frantic Prenton Park finale.
But it was Hume who proved the difference in a pulsating finish to move Doncaster into the top six as Tranmere were made to rue a number of earlier missed opportunities following Saturday's defeat at Bournemouth.
Andy Robinson's early strike drifted just shy of the top corner and Ben Gibson's header flashed inches wide but it was Doncaster who almost struck first when Paynter's 25th minute header hit the underside of the Tranmere crossbar.
Gary Woods made a fingertip save to deny a superb curling shot from Robinson but Paynter struck three minutes after the interval, bringing the ball down inside the area and poking it into the far corner.
Cassidy levelled matters three minutes from time amidst a crescendo of noise, but Hume had the final say to delight Doncaster's legion of travelling fans.