Dunfermline 0-2 Hearts
Goals from Andy Webster and Rudi Skacel eased Hearts to victory over a toothless Dunfermline at East End Park.
Hearts had the best of a dull first half before Webster headed past Paul Gallacher just before the break.
Dunfermline improved after the break without seriously threatening goalkeeper Marian Kello.
David Templeton was Hearts' danger man on the break and came close himself before setting up Skacel to fire home after 76 minutes.
Victory kept Hearts in fourth spot in the Scottish Premier League, with the Pars still a point ahead of bottom side Inverness Caley Thistle.
Andy Kirk had returned to Dunfermline's starting line-up, replacing Andrew Barrowman, who has undergone an appendix operation, as manager Jim McIntyre made four changes from the side that was so disappointing in a 4-0 defeat by Aberdeen.
On-loan right-back Jason Thomson was unable to face his parent club, while Alex Keddie and Craig Easton also dropped out, with Paddy Boyle, Joe Cardle and Ryan Thomson coming into the side.
Fit-again Marian Kello replaced Jamie McDonald in the Hearts goal despite the latter's clean sheet in the win over Celtic.
Kirk just failed to test the keeper within seconds of kick-off, the former Hearts striker unable to get enough of a touch on a Cardle free-kick.
However, Hearts quickly exerted midfield control and David Templeton's burst into the penalty box and low drive just evaded the back post thanks to a last-ditch deflection from John Potter.
The visitors suffered a blow on 22 minutes when Ian Black suffered a leg injury and the tenacious midfielder was replaced with the more silky skills of Mehdi Taouil.
It descended into a dour midfield battle until Skacel forced goalkeeper Paul Gallacher to touch his low drive from 20 yards past the post.
Danny Grainger appeared to mis-hit the resulting corner and, when Kirk failed with his attempt to clear at the front post, Webster stooped to head past the goalkeeper from six yards.
Dunfermline improved in terms of territory and possession after the break, but Hearts remained the more dangerous side and Ryan Stevenson headed straight at Gallacher from eight yards.
It took an individual effort from David Graham to threaten Hearts' goal, the winger going on a mazy run into the box, but his shot from an acute angle was easily held by Kello.
Boyle curled a long-range effort over Hearts' crossbar, but the emerging Pars threat was quickly extinguished as the visitors exposed space behind the full back.
Templeton had already curled an effort wide of the far post when, from a similar position, his low effort deflected off Gallacher and Skacel, who had himself set up the winger, fired into the unprotected net.