For the Cappielow club, the defeat completed a miserable four-game losing run which ensured they would finish in seventh position - one place below Allan Moore's pre-season target.
The Ton boss went with a 4-4-2 formation comprised of players who, with the exception of loanee Grant Evans, are likely to be with the club again next season, while there was also a place on the bench for youth star Declan McDaid.
And there was no indication of the eventual outcome as Morton made a good start. They could have put the game to bed in the first half but for some inspired goalkeeping by Scott Christie.
The Stirling custodian had to look lively as he thwarted Peter Weatherson, Allan Jenkins, Carlo Monti, Brian Graham and David O'Brien with a series of fine stops in the opening 15 minutes.
The hosts, meanwhile, were demonstrating why they had gone so long without securing victory, as they barely managed to get over the halfway line.
When they eventually managed to fashion an opportunity in the 20th minute, Michael Mullen dragged a woeful angled drive across the face of goal.
Morton finally took the lead their play merited in the 28th minute, when Stirling sub Michael Doyle clipped O'Brien's heels inside the box and Monti sent Christie the wrong way with a cool penalty.
But the match was turned on its head as Stirling scored twice in a frenetic first-half finale.
As Ton defenders converged on Sean Stirling, he slipped the ball through an opening for Ross Forsyth and stayed on his own course down the middle to sweep the cut-back beyond Colin Stewart to restore parity in the 42nd minute.
Then, in first-half injury time, the Binos were awarded a penalty when Evans felled Stirling with a clumsy challenge inside the six-yard box.
Stirling picked himself up and thrashed his spot-kick to Stewart's left. The Ton goalkeeper plunged to block, and had actually saved the kick until he knocked the ball into the net with his elbow for a bizarre own goal.
The two-goal salvo rocked Morton, and they should have gone further behind five minutes after the restart, but the inrushing Michael Mullen somehow managed to divert Paul McHale's cut-back wide from point-blank range.
The visitors would not be outdone, and missed a glaring opportunity in the 55th minute when a Tidser drive broke perfectly for Graham, who blazed horribly over the crossbar from six yards.
Graham's miss led to an exchange of words with heckling fans, while Jenkins also reacted to criticism from the stands as a hostile atmosphere began to build in the away end.
Ton had Stewart to thank for keeping a lid on things when he threw up a strong arm to block Gordon Smith's rising drive.
But it was Albion who scored again in the 88th minute when Mullen rounded Stewart and rolled into an empty net after Graeme Holmes had sent him through on goal with a poorly-directed slide tackle.
Although Stuart McCaffrey headed home a Stewart Kean corner in injury time to make it 3-2, it was too late to salvage a draw or to prevent a season which had provided encouraging signs from ending in huge disappointment.