Both gathered full points from their latest matches, Morton seeing off Falkirk 2-0 at Cappielow and Partick having to work hard to defeat Dumbarton 3-0 at Firhill.
Morton kept their two-point advantage after Archie Campbell put them in front from Peter MacDonald's pass.
MacDonald headed a second goal early in the second half from Michael Tidser's cross and managerless Falkirk could not match their cutting edge.
Partick survived an early scare in their match with Dumbarton when Garry Fleming beat Scott Fox only to see his 20-yard shot strike the post.
The home side heeded the warning and snatched a ninth-minute lead when Steven Lawless volleyed home after Steven Craig had headed the ball down.
Mark Gilhaney was denied by Fox as Dumbarton hit back and Ian Murray's side matched Partick for long spells.
Lawless eventually scored his second with a tremendous finish after 74 minutes and Kris Doolan removed any doubt when he prodded home with nine minutes left.
On a day when the top three all collected full points, Livingston enjoyed a comfortable 2-0 away win at Raith Rovers.
Livingston had the upper hand throughout with Iain Russell putting them in front from the penalty spot after Eddie Malone handled in the 19th minute.
Stefan Scougall scored a second before half-time with the aid of a deflection and, in truth, Raith could not muster much in response in the second half.
Hamilton took a valuable point at Central Park as they held Cowdenbeath 1-1 to maintain their three-point advantage over the Fife side in the lower reaches of the table and ease any relegation concerns.
Billy Reid's side looked menacing throughout and Ziggy Gordon had a decent effort which Colin Stewart touched onto the post and past for a corner in the early exchanges.
Stevie May broke the deadlock after 32 minutes when he tucked the ball under Stewart.
However, Cowdenbeath were level before half-time when Craig Moore headed home.
Both sides had chances to win it in the second half and May should have done better when he produced a rather tame finish from a good position, while Andy Ryan also went close for Hamilton later in the half.
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