Peter MacDonald's double was the difference as Morton prevailed in an end-to-end encounter against Falkirk.
MacDonald gave the hosts an early lead with a header from Sean Fitzharris' delivery, but David Weatherston volleyed in an equaliser soon after.
Blair Alston then stroked the Bairns into a half-time lead.
MacDonald powered in a penalty after a trip on Andy Jackson and Jackson later headed home a Fitzharris cross to keep the Greenock side top of the table.
Morton: Stewart, Evans, Graham (Campbell 81), McCaffrey (McCann 63),Forsyth, Fitzharris (McGeouch 84), Smyth, Bachirou, O'Brien, MacDonald, Jackson. Subs Not Used: McGinley, Weatherson.
Booked: MacDonald, Smyth, Forsyth. Goals: MacDonald 6,54 pen, Jackson 58.
Falkirk: McGovern, Duffie, Dods, Wallace (Rhys Bennett 29), Scobbie, Alston (Jay Fulton 76), Mark Millar, Murdoch, Weatherston (Sibbald 59), Higginbotham, El Alagui. Subs Not Used: Bowman, Graham.
Booked: Rhys Bennett. Goals: Weatherston 17, Alston 24.
Ref: Crawford Allan