After seven minutes an excellent ball over the top from Scott Severin released Kevin McNaughton wide on the right, however his deep ball failed to pick out Darren Mackie lurking at the far post.
With Aberdeen hemming Hearts back it was Richie Byrne who was just off target with his speculative 30-yard effort.
Aberdeen forced a series of corners midway through the half but efforts from Zander Diamond and Severin failed to trouble Craig Gordon in the Hearts goal.
Hearts showed they weren't just making up the numbers when neat interplay between and Dennis Wyness and Lee Miller saw the latter's cleaver effort finger-tipped away by Ryan Esson at the expense of a corner.
Just after the half-hour mark a McNaughton cross evaded Gordon in the Hearts goal, from an acute angle Byrne forced the ball back across the area to find Phil McGuire, whose fierce effort from 12 yards crashed off a post and away to safety.
After 35 minutes McNaughton came to the home side's rescue, heading the ball off the line after Esson had flapped at a Robbie Neilson cross.
Aberdeen finally got the goal they richly deserved in the final minute of the half. Severin's neat free-kick into the area found Byrne sneaking in behind Craig Sives to nod the ball beyond Gordon from six yards.
A snap shot from Miller after the restart had Esson scrambling across his goalmouth but the effort was narrowly off target.
Aberdeen forced a corner at the other end which led to them extending their lead after 48 minutes. Severin's corner found the head of sub Lubomir Blaha, whose effort ricocheted off Derek Adams and into the net.
The Dons almost made it three soon after. Ben Muirhead was given acres of space on the left, carrying the ball 30 yards to the edge of the penalty box before knocking the ball into the danger zone, where Blaha was only a fraction away from getting a touch.
Hearts' Lithuanian midfielder Saulius Mikoliunas almost brought his side back into the game on the hour.
He raced unopposed into the Dons box, but from 14 yards his left-foot effort skidded wide of the upright.
Visiting keeper Gordon broke the hearts of the home support after 77 minutes when he made a miracle save to deny Mackie.
Minutes later Gordon again produced a brilliant save, this time tipping a McNaughton header over the bar as the home side went for broke, but it counted for little at the final whistle.