The Leith side were happy to soak up the pressure in the second half and even when the hosts breached their rearguard, goalkeeper Ofir Marciano was on hand to repel the danger.
The result will raise questions over Hearts manager Daniel Stendel's decision to return to Germany for personal reasons prior to the game and give the squad Christmas Day off.
It was a memorable afternoon for Hibs, however, as the Easter Road side moved 13 points clear of their city rivals.
Hearts' position at the Ladbrokes Premiership basement ensured the hosts were desperate for points and a first victory under new manager Stendel.
But the Gorgie outfit got off to a nightmare start when Boyle volleyed Hibs in front inside six minutes.
Scott Allan lifted a hopeful ball inside the area and Boyle peeled off Christophe Berra before placing a measured first-time shot past goalkeeper Joel Pereira.
The away end erupted in celebration and immediately began to taunt their city counterparts with chants of 'Hearts are going down'.
There was further alarm for Hearts when Vykintas Slikva was allowed time to fire over before an Allan corner glanced off Pereira's bar.
Hearts have recently struggled for creativity in the final third but Ryo Meshino at least registered a shot on target with a right-footed drive from outside the box that was straight at Marciano.
Hibs' afternoon got even better in the 31st minute when Boyle added his second. Allan poked the ball off the feet of Loic Damour in midfield and Boyle raced clear of the Hearts rearguard before coolly slotting past Pereira.
Meshino offered some hope of a comeback minutes later with a drive from distance that forced Marciano into a stunning save.
Hearts boss Stendel made two changes at the break, Euan Henderson and Oliver Bozanic replacing Aidy White and Damour.
There was no immediate upturn in the home side's fortunes, however, with Hearts blunt in attack.
Meshino continued to look the most likely to score but Marciano pulled off another fine save to deny the Japanese playmaker, this time getting down to a right-footed shot from 20 yards.
Uche Ikpeazu was then picked out by Sean Clare inside the area but the striker pulled his shot wide from a tight angle.
Hearts were piling on the pressure. Clare set up Henderson but the sub was denied by a double save from Marciano and the Israel international got his clean sheet.