Farid El Alagui's goal kept Falkirk second in Scottish Football League Division One as Morton were narrowly defeated.
Morton almost took the lead when Darren McGeouch's drilled effort was well tipped around the post by Michael McGovern.
McGeouch tried his luck from long range towards the end of the first half, but McGovern again made the save.
The Bairns moved ahead on 58 minutes when David Weatherston's pinpoint cross found El Alagui and the striker slammed his effort into the roof of the net.
McGovern came to Falkirk's rescue again late on, punching Peter MacDonald's powerful effort clear.
Falkirk: McGovern, Duffie, Dods, Wallace, Scobbie, Jay Fulton (Weatherston 55), Murdoch, Mark Millar, Sibbald (Kingsley 69), El Alagui, Higginbotham (Rhys Bennett 89). Subs Not Used: Bowman, Alston.
Goals: El Alagui 58.
Morton: Cervi, Evans, Smyth, Graham, O'Ware, Di Giacomo (Fitzharris 74), Derek Young, McGeouch, O'Brien, Jackson (MacDonald 74), Weatherson (Campbell 74). Subs Not Used: Deans, McCann.
Ref: Iain Brines