Falkirk missed an opportunity to leapfrog Dundee into second place as Morton eased their relegation worries and inched Ross County yet closer to the Division One title and promotion in the process.
The Bairns' defeat, combined with Dundee's 3-1 loss away to Hamilton Academical, leaves County 15 points clear at the top with only eight games remaining.
Michael Tidser netted his eighth goal of the season to give the depleted visitors the lead in the 53rd minute with a smart finish from the centre of the penalty area.
Derek Young could have doubled Morton's lead 15 minutes later, but Falkirk goalkeeper Michael McGovern was equal to his soft header.
Rhys Bennett was then on hand to clear Andy Graham's close-range header from David O'Brien's corner.
Morton eventually doubled their lead eight minutes from time when Archie Campbell slotted home from 12 yards to make sure of the points and only a second win in 11 games.
Victory moves the Greenock side six points clear of Raith Rovers, who occupy the relegation play-off spot, although the second-bottom side have a game in hand.
Falkirk: McGovern, Murdoch (Rhys Bennett 45), Dods, Wallace, Scobbie, Weatherston, Mark Millar, Fulton, Gibson, Alston (Faulds 71), White (Kingsley 60). Subs Not Used: Bowman, Dick.
Morton: Combe, Graham, Evans, Smyth, Forsyth, Derek Young, Bachirou, Tidser, O'Brien, MacDonald, Campbell. Subs Not Used: McGinley, Jackson, McGeouch, O'Ware, Flannigan.
Goals: Tidser 56, Campbell 82.
Ref: Euan Norris