Stephen Elliott netted from close range after three minutes for the hosts, whose players on Friday submitted an official complaint to the Scottish Premier League after a third successive month when their wages failed to arrive on time.
Mehdi Taouil struck after 27 minutes, David Templeton after 71 minutes and substitute Rudi Skacel headed a stoppage-time fourth as Hearts lifted at least some of the gloom which has descended on Tynecastle in recent weeks.
The win saw Hearts, who have been put up for sale by owner Vladimir Romanov, consolidate fifth place in the table, but next week's visit of third-placed Motherwell will prove a test of their ability and spirit.
A draw for Dunfermline would have taken them off the foot of the table after Hibernian lost at Aberdeen, but their near 22-year wait for a win at Tynecastle goes on and they will need to show more fight and quality in their battle for survival, which continues at home to St Johnstone next week.
Hearts beat the Pars 2-0 on October 15 before their wage impasse began, with their October salary received on November 4.
Their November wage was paid 29 days late on Thursday, but December's pay date on Friday went by without further funds and PFA Scotland submitted an official complaint to the SPL on the players' behalf as the Hearts squad finally showed they were willing to fight the issue.
Hearts performed well in losing 1-0 at title-chasing Celtic last weekend, but manager Paulo Sergio expressed doubt whether his troops could rise to the occasion against the Pars amid the turmoil.
After three minutes, the concerns of Sergio - serving the final game of a five-match touchline ban - were allayed as Hearts went ahead.
Ian Black's corner found Ryan McGowan, who scuffed an attempt on goal.
However, Elliott was on hand to turn the ball in, with the Pars players stationary in the box.
Dunfermline had chances to respond swiftly, but Andy Barrowman, Paul Willis, Alex Keddie and David Graham all failed to test Marian Kello.
Hearts were finding their rhythm and Templeton forced Paul Gallacher into a smart save before Taouil curled an effort narrowly over.
Two minutes later, with Dunfermline again backing off, Taouil hit another shot from the edge of the area less cleanly, but the right-footed effort was good enough to put Hearts 2-0 up.
Barrowman headed over from a corner before Marius Zaliukas missed a free header and the chance to put his side further ahead at the interval.
Kello saved well from Liam Buchanan, turning the Pars striker's header around the post for a corner before Hearts came close again.
Taouil dispossessed Martin Hardie in midfield before feeding Elliott, who shot into the side-netting.
Templeton shot wide from Taouil's cross and was then twice denied by Gallacher.
After Andy Webster was booked for arguing he had been brought down in the visitors' box, a third goal arrived, with Templeton's persistence rewarded.
The winger waltzed around the Pars defence to find an opening before curling right-footed inside the post for his first goal of 2011, his last strike coming last December at St Mirren.
Keddie headed over from a corner before Skacel fired wide from fellow substitute Arvydas Novikovas' cross at the other end.
Replacement Ryan Stevenson's shot was parried by Gallacher and Skacel headed in the rebound in the second minute of stoppage time to complete the rout.