Brian Graham's first-half strike sent them four points clear of Falkirk and Cove Rangers with three games remaining.
Graham got the winner as he was first to react after Shea Gordon's header hit the crossbar from a corner.
Falkirk – who parted company with management duo Lee Miller and David McCracken earlier in the week – and Cove Rangers both lost ground after they played out a 2-2 draw.
Callumn Morrison put Falkirk ahead from the spot but Leighton McIntosh's effort sent the sides into the interval all square.
Mitchel Megginson then put Rangers ahead before Conor Sammon ensured the points were shared four minutes from the end.
Aaron Steele's 67th-minute strike earned East Fife a 2-1 win over Dumbarton, while two goals from Hamish Ritchie helped 10-man Peterhead to a comfortable 3-0 win over Clyde.