A dramatic injury time goal from Corey Blackett-Taylor clinched Tranmere a first league win in over two months as the Birkenhead club battles to avoid relegation.
Without a victory since December 21, Rovers romped into an early 2-0 lead courtesy of goals from Mark Ellis and Alex Woodyard.
But the Shrews hit back after the break through an Aaron Pierre header before Calum Lang levelled the scores up just past the hour mark.
Tranmere looked to have blown their chance of victory, with chances missed at both ends of the pitch, but deep into injury time, Blackett-Taylor latched onto a long ball forward from Scott Davies and drilled a left-footed shot that nesstled into the bottom corner, sending the travelling Super White Army wild with delight.
The result reduces the gap between Rovers and AFC Wimbledon to five points with Tranmere still having a game in hand.
They next face promotion-chasing Fleetwood Town at home, where they will be looking to build on this superb morale-boosting away win.
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