With Nicolas Caraux out with a groin injury, Derek Gaston, pictured, was back between the sticks despite starting against Alloa at the weekend.
And the former Albion Rovers custodian kept his side in the game early on with a hat-trick of fine reaction saves to deny Sean Murphy, ex-Ton midfielder Kyle Wilkie and Kyler Lander.
He started the second half in a similar fashion, thwarting George Hunter with another solid stop on 49 minutes.
But it was Ton who got their noses in front 60 seconds later from the penalty spot after teenage striker Jack Smith, who made his first-team debut against Alloa, was fouled by Shaun Rutherford.
The Livi left-back was sent packing for denying a goal-scoring opportunity, and Joe McKee compounded their problems by rifling home the penalty. He struck the kick with such power that goalkeeper Kevin Walker required treatment after getting a hand to the ball before it slammed into the top left-hand corner.
The game went through a 20-minute lull until David Hopkin’s men stepped up through the gears in the final 10 minutes.
Aidan Fulton crashed a stunning shot against the crossbar, Smith went close on a two separate occasions, and skipper Dougie Imrie was just out with an audacious chip from the half-way line. And Imrie, who played the full 90 minutes due to being suspended for Saturday’s trip to Dundee, sealed the points in the third minute of stoppage time, rifling home a fierce drive from 22 yards.
Morton (4-1-2-1-2): Gaston (8); Knight (6), Jamieson (6) (Irvine 76, 3), O’Ware (7), Russell (6); Imrie (7); O’Brien (6) (Lamont 67, 3), Fulton (6); McKee (6) (O’Neil 61, 5); Smith (7), McNeil (7).