The home side began brightly and had chances to take the lead but failed to capitalise on their chances and the Edinburgh side took full advantage.
Osman Sow grabbed the opener before Hearts doubled their lead just three minutes later through Prince Buaben.
Jordan McGhee then wrapped up the victory just before the hour mark as Robbie Neilson’s side secured their seventh league win from eight matches.
The Edinburgh side almost fell behind in the opening exchanges though, a poor backpass allowing Gavin Reilly in only for the striker to shoot wide.
Andy Dowie then went even closer for the home side as he headed against the post but that was where the positive news ended for them.
Hearts began to force their way into the game and took the lead through Sow after 39 minutes, as he controlled the ball with his chest, spun and volleyed in off the crossbar from the edge of the area.
Buaben then doubled the away side’s lead in style, capping an impressive solo run by slotting past goalkeeper Zander Clark just three minutes later to give them a 2-0 half-time lead.
The hosts survived a penalty shout five minutes after the restart but Hearts’ appeals went unheeded.
It was not to prove crucial to the outcome, however, as McGhee put the result beyond doubt on 59 minutes, the defender converting a Billy King cross from close range.
Queen of the South continued to battle hard without to create any clear-cut chances and instead Hearts went close to adding another when substitute Miguel Pallardo almost scored on his debut, only to be denied by Clark.
Sow then shot into the side-netting in the closing stages before the same player forced Clark into another save as he kept out the striker’s curling shot from inside the area.