The game had been a fairly even contest up until midfielder Joe McKee was forced off and stretchered down the tunnel with badly sprained ankle ligaments on 38 minutes.
Although the formation remained the same, the reshuffle - Reece Hands moved infield, Dougie Imrie switched to the right and sub David O'Brien came in on the left - unsettled Ton.
They conceded just two minutes later when a David McNeil shot was blocked and ricocheted back into the Morton half, catching the midfield pushing up.
Jay Fulton picked up possession and slipped Phil Roberts in goal. Derek Gaston made a superb save low to his left but Rory Loy had followed up and swept home the loose ball to open the scoring.
To concede five minutes from the break was a blow, but to concede a second one minute into first half stoppage time was a killer, particularly as it was all of Morton's own doing.
Gaston took a risky free-kick out across the defence to Michal Habai on the right but found his target. However, instead of taking a touch the Slovak let the ball run across his body.
Loy pounced on the lax play, stealing possession before driving in and slotting past the out of position Gaston for 2-0.
The final nail was hammered in the coffin just two minutes after the restart when more disastrous defending from Habai saw him leap in behind Mark McLaughlin to challenge for the same header.
The collision meant neither managed to head clear and the ball dropped for Phil Roberts, who breezed across the edge of the box before lashing high into the top-left corner.
Ton's only real goalscoring threat for much of the match came from a series of long-range strikes from Hands.
The Englishman pulled one back with a drilled effort from 25 yards on 90 minutes but it was too little, too late for the visitors who deservedly left Falkirk empty handed.
Morton (4-4-2): Gaston; Taggart, Habai, McLaughlin ©, Fitzpatrick; Hands, Bachirou, McKee (O'Brien, 38), Imrie; Campbell (Fulton, 78), McNeil (Wallace, 60).
Subs not used: Page, Caraux (gk).
Booked: McLaughlin (67)
Falkirk (4-1-3-2): McGovern ©; Duffie, Vaulks, Kingsley (Dick, 52), Turnbull; Durojaiye; McGrandles (Sibbald, 64), Fulton (Grant, 75), Alston; Loy, Roberts.
Subs not used: Leahy, Bowman (gk).
Booked: Fulton (5).
Referee: Craig Thomson