Nathan Austin scored the winning goal 10 minutes from time after Dunfermline goalkeeper Ryan Scully spilled the ball.
Lawrence Shankland had given Dunfermline the lead midway through the first half when he tucked the ball home at the near post from Ryan Williamson's cutback.
But East Fife equalised through Liam Buchanan in the 56th minute after he went down in the penalty area as a result of a challenge from Alex Whittle.
It looked a soft award but Buchanan sent Scully the wrong way from the spot and East Fife did not look back, with Austin earning them a valuable three points when his strike went in off the post.
Airdrieonians had the most emphatic win of the day, thumping Forfar Athletic 5-1. Gregor Buchanan, Jamie Bain and Keigan Parker had them 3-0 ahead after 22 minutes. Forfar had Iain Campbell red-carded after 35 minutes. Dale Hilson pulled a goal back but Jim Lister and Liam Watt emphasised Airdrie's superiority with second-half goals.
Ten-man Ayr United won their third successive match, beating Arbroath 2-1 at Somerset Park. Craig Malcolm gave Ayr an early lead but Michael Donald of the hosts was sent off midway through the first half. Kenny Deuchar equalised but Ayr were back in front before half-time when Michael Moffat netted what proved to be the winner.
Stranraer and Stenhousemuir drew 1-1. Jamie Longworth put Stranraer ahead but the home side suffered a setback early in the second half when Stephen Stirling was sent off. Stenhousemuir made them pay when David Rowson equalised in injury time.