Hearts overcame Dunfermline 2-1 in the Clydesdale Bank Premier League to leave the Pars still searching for their first home league victory of the season.
The rock-bottom Fifers are now six points behind Hibernian with only five games left to play - an advantage Hibs could extend on Sunday with their home encounter against Motherwell.
Gary Glen and Darren Barr scored within three minutes of each other at the start of a disastrous second half for the home side. Hearts seemed to be coasting to victory before a late Marius Zaliukas own goal ensured a nervy final 10 minutes, but the visitors held on.
The hosts had the game's first meaningful opportunity but Andy Kirk could only nod Austin McCann's left-wing cross over the bar. Jefferies's men continued to press and Kirk was unlucky to see an ambitious effort from the corner of the penalty area swerve just past the front post.
On the stroke of half-time the visitors passed up the best chance from the opening 45 minutes. Austin McCann's attempt to head the ball back to Chris Smith came up short with Glen intercepting and trying to round the goalkeeper. The striker managed to knock the ball past Smith but put too much on the touch and Dunfermline were able to clear.
Hearts' first-half performance reinforced the theory they were just at East End Park to make up the numbers; the game being supposedly meaningless for Hearts with little left to fight for in the league and a cup semi-final on the horizon. However, the opening six minutes of the second half erased that notion.
Three minutes after the restart a Scott Robinson cross was knocked down for Rudi Skacel to unleash a first-time volley that stung the palms of Smith and went out for a corner. From the resulting set-piece, Dunfermline failed to clear and Glen was able to slide the ball into the far corner of the net from a tight angle.
Three minutes later Hearts had another. Ryan McGowan's header at the back post was cleared off the line by Alex Keddie, but when the ball was knocked back into the six yard box the defender lost the aerial battle with his counterpart Barr who headed Hearts into a two-goal advantage.
The match looked to be petering out to an inevitable conclusion until suddenly Dunfermline found themselves back in with a chance. A cross to the back post found substitute Cardle in space. The winger fired the ball back across goal and appeared to be turned in via a deflection off Hearts captain Zaliukas.
The full time whistle appeared imminent when Dunfermline were awarded a free-kick right on the edge of the penalty area, but Joe Cardle could only lift his effort over the crossbar.