BBC
A header from Andrius Velicka ended Hearts' 10-game run without a win and claimed the Edinburgh derby honours.
The Lithuanian's nod from six yards after 20 minutes was straight at Yves Ma-Kalambay but the Hibs keeper could only flap the ball into his own net.
With both sides struggling at the wrong end of the table, there was a real shortage of quality play.
However, Hearts posed more threat in attack, while Hibs seldom caused the home defence any trouble.
Hearts will be delighted with a rare victory and to have kept just their second clean sheet of the season.