Wednesday also had substitute Zigor Aranalde sent off after Chris Brunt had given the Hillsborough side the lead from the penalty spot.
Wednesday, still reeling from a midweek defeat at Huddersfield which ended their hopes of automatic promotion, were in trouble in the 11th minute after centre-back Richard Wood blundered.
Paul Hall steamed on to the loose ball but the big defender recovered quickly to block the little striker as he was about to shoot .
Wednesday broke rapidly as quick-thinking Glenn Whelan came close to snatching the opener. John Achterberg came charging off his line to clear under pressure from Graham Barrett and Whelan lobbed the ball towards the empty net from 30 yards out but it curled inches wide.
Barrett, on loan from Coventry, went close minutes later. Brunt's deep cross was headed into the goalmouth by Jon Paul McGovern and Barrett's stinging volley was blocked by Ian Goodison.
The breakthrough came in the 30th minute after Mark Rankine chopped him down on the edge of the box and Brunt powered his spot kick beyond Achterberg.
Tranmere were level three minutes before the interval when centre-back Michael Jackson produced a towering header to steer Jason McAteer's free-kick into the top right-hand corner.
The lively Barrett lashed a low shot across the face of the Tranmere goal before Wednesday were reduced to 10 men in the 55th minute. Aranalde, on at half time for the injured Wood, was red carded for elbowing Goodison.
Iain Hume added Tranmere's second five minutes later by stabbing in Theodore Whitmore's low cross after holding off Brunt's despairing challenge.