Rangers took full advantage of the current turmoil at Tynecastle as a late goal from Nacho Novo gave them victory.
The striker's speculative 78th minute shot from outside the box took a deflection to carry it beyond Craig Gordon and into the bottom corner of the net.
It proved the only goal of a bruising game which produced seven yellow cards - five of them for Rangers.
Hearts left Steven Pressley on the bench after he walked out before the previous match against Falkirk and Paul Hartley took over the captain's armband.
Rangers had the first chance and Alan Hutton should have done better when Dado Prso headed the ball across goal but he could not steer his effort on target.
Hearts hit back and Andrius Velicka shot narrowly wide after Jamie Mole had set him up.
The game became bogged down in midfield with chances few and far between with neither side particularly dominant.
Novo had the best effort of the first half with a shot low to Gordon's left but the Scotland goalkeeper managed to turn the ball past his post.
Julien Brellier had Hearts' only first-half effort on target but his shot from distance was easily dealt with by Allan McGregor.
Prso had a couple of chances to break the deadlock before the interval. He headed narrowly over from a corner and then, just two minutes from the break, shot just inches wide after good work from Novo.
Velicka had a chance at the start of the second half but McGregor managed to block the ball and divert it for a corner.
Barry Ferguson was then denied at the other end by Gordon as it seemed only a matter of time before a goal came.
Hartley almost caught out McGregor with a cross which struck the outside of the post but Rangers survived.
There was a flashpoint in the 57th minute after Novo was booked and a missile was thrown on to the pitch from a section of the Rangers' support and police moved in to defuse the situation.
Kris Boyd missed a great chance for Rangers after 66 minutes when he shot straight at Gordon when he had the goal at his mercy.
The goal finally arrived with 12 minutes left when Novo was allowed to run unchallenged and he whipped a low shot past Gordon with the aid of a deflection.