Ian Cathro suffered a defeat on his Hearts managerial debut, as goals from Rob Kiernan and Barrie McKay secured a 2-0 win for Rangers at Ibrox on Saturday.
Rangers started the game the brighter and almost took the lead as early as the 13th minute when McKay's corner fell to Lee Wallace on the edge of the area and the the left-back drove a low effort just wide.
Mark Warburton's side should have taken the lead two minutes later when Kenny Miller was sent clean through by defender Danny Wilson, but though he succeeded in lifting the ball over onrushing Hearts goalkeeper Jack Hamilton, the Gers forward slipped the ball wide.
Hearts had the ball in the net less than a minute later through Don Cowie, but the offside flag ruled it out amid protests from several Hearts players.
Wes Foderingham was then called upon in the Rangers goal to keep the scores level when he made a save from close range once again from Cowie.
Rangers soon recovered to take the lead through centre-back Kiernan.
Jason Holt was brought down by Patterson on the left hand side and the resulting free-kick was fizzed in by James Tavernier, with Kiernan steering his header past Hamilton.
The lead was doubled just five minutes into the second half when McKay dispatched Wallace's long throw to put the Gers in control.
The victory keeps Rangers in second position in the table behind league leaders Celtic, while Hearts remain in fourth.
Rangers next travel to Hamilton Academical in the Scottish Premiership on Friday while Hearts face Partick Thistle next Saturday.