The visitors took the lead just after the hour mark when Chris Hussey found Soares in the box who poked home, sparking wild scenes from the travelling fans.
The Shakers have finished the season with eight consecutive away wins and, with Southend losing at Morecambe, David Flitcroft’s side return to League One at the second time of asking.
Max Power had the ball in the net for Tranmere on 18 minutes, but his effort was chalked off for handball.
On the stroke of half time Owain Fon Williams thwarted efforts from Soares and Andrew Tutte in quick succession.
The Shakers had appeals for a penalty waved away just before the hour mark, but there was a partial pitch invasion moments later as Soares broke the deadlock.
Rory Donnelly missed a great chance to equalise for Rovers with 15 minutes left when he headed wide with the goal at his mercy and Bury held on for the crucial win and a third-place finish.