The home side dominated long stages of the game against their lower-ranked opponents but could not find the killer touch in front of goal, and now sit fourth in the league.
Jordan Moore and Josh Falkingham both missed with headers and Stephen Husband tried his luck from 30 yards but his shot flew a yard over Greg Paterson's crossbar.
Dunfermline took a deserved lead two minutes from the half-time break when the East Fife defence backed off invitingly and Husband slotted home the ball from 15 yards.
But East Fife hit back in the second half and killed off the Pars with a quick one-two.
Substitute Cedric Tuta back-heeled the ball for midfielder Ross Brown to equalise with a left-foot shot.
Three minutes later, striker Liam Buchanan then scored the winner against his former club with a curling 25-yard shot.
Stenhousemuir slipped to a 10-point deficit behind league leaders Rangers with a 1-0 defeat against Stranraer at Stair Park.
Midfielder Chris Aitken, with his ninth goal of the campaign, settled it with a penalty late in the second half.
Airdrieonians remain at the bottom of the table after Forfar Athletic won 2-0 in Lanarkshire.
Trialist Jamie McCluskey put Forfar ahead after 13 minutes and Ross Campbell settled it with a penalty in injury time after a foul on striker Chris Templeman.
Ayr United climbed to third place by beating Arbroath 2-0, with Kevin Kyle and Adam Hunter contributing the goals in each half.