A late penalty from skipper Steven Pressley gave Hearts a merited victory at Tynecastle.
Hearts had already had two strong penalty claims turned down before Alexander Diamond felled Mark De Vries in the area with only nine minutes left and Pressley kept his cool to secure the victory.
It was no more than Hearts deserved as they had dominated without being convincing in front of goal.
Hearts created the first chance after six minutes when Robert Sloan whipped in a free-kick which Patrick Kisnorbo volleyed over from close range.
Five minutes later, De Vries also stood accused of being wasteful in front of goal when Joe Hamill picked him out on the edge of the six-yard box but his downward header bounced over the crossbar.
For all Hearts' dominance, David Preece was not unduly troubled in the first half. He dived low to gather a shot from De Vries which threatened to creep in at his left-hand post and then he had to react smartly to clutch a header from Phil Stamp.
Paul Hartley and Stamp also failed to hit the target when they were well-placed and Aberdeen were the happier to be goalless at half-time.
Hearts also had a strong penalty claim turned down two minutes from half-time when Kevin McNaughton looked to catch Hartley but the referee saw nothing wrong with the challenge.
Aberdeen had a couple of half-hearted efforts from Scott Morrison as Pressley took charge of most things for Hearts at the back.
De Vries had another chance to put Hearts in front two minutes into the second half after substitute Robbie Neilson put him through but he thrashed his shot well over the top.
But Aberdeen hit back and Leigh Hinds shot inches wide of the far post after shrugging off the attentions of Kisnorbo.
Hearts had another penalty claim turned away when De Vries tumbled under a challenge from Russell Anderson but the referee looked to be correct this time.
Preece then produced the save of the match to slap a 20-yard shot from Kisnorbo past his right-hand post.
Hearts had a let-off when David Zdrilic shot sloppily after Kisnorbo had given the ball away inside his own half.
The home side finally claimed the points when Diamond pulled down De Vries and Pressley calmly slotted home the penalty kick.