The Jambos are aiming to end the 40-year dominance of Glasgow giants Celtic and Rangers and have amassed a large early-season lead after taking 25 from a possible 27 points in their opening nine games.
However, they have now won just once in their last four to allow the Old Firm to close in.
Celtic are four points adrift, with Rangers nine off the top. Both have played a game fewer than Hearts.
The visitors were without captain Lawrence Shankland through injury.
Shankland had been one of Scotland's goalscoring heroes in qualifying for the World Cup for the first time since 1998 this week and his predatory instincts were missed at Pittodrie as Hearts missed a series of chances to level in the second half.
Topi Keskinen scored the only goal as the Finnish winger cut inside to fire into the far corner just before half-time.
Tomas Magnusson and Claudio Braga fired too close to Dimitar Mitov after the break as Derek McInnes suffered a first defeat as Hearts boss in 18 games in charge.