With Celtic losing to Motherwell last night this match provided Rangers with the perfect opportunity to go top of the league for the first time this season. However the Ibrox side made heavy weather of it before finally winning to remain the only undefeated team in the league.
A diving header from Claudio Caniggia just before half time and a late Shota Arvaladze goal were the difference between the teams although Hearts can point to two efforts that hit the woodwork.
Rangers went on the attack from the first whistle and both Arveladze and Barry Ferguson went close before the home team squandered a wonderful chance in the 12th minute. Robert Malcolm's through-ball beat the Hearts off-side trap but from Caniggia's cross Arveladze failed to control the ball before Ronald de Boer blasted his shot over.
Hearts nearly took the lead, but Phil stamps header from a Jean Lois Valois cross that clipped the top of the bar on the way over. The visitors again went close when Kevin McKenna headed a Valois corner against the post with Rangers keeper Stefan Klos stranded.
Rangers were beginning to look very rattled until Caniggia stepped in to settle their nerves. De Boer showed marvellous skill in curling a cross behind Paul McMullen that Caniggia buried in the net from six yards.
Rangers were still guilty of wasting good possession at the start of the second half although Craig Moore nearly added to the home sides lead, but his header a corner came back off the face of the bar.
With such a slender lead, the home side could never relax and Mark De Vreis nearly equalised for the visitors with a header that went narrowly over.
Rangers wrapped up the points near the end with a rather fortunate goal. The cross from substitute Billie Dodds landed behind Caniggia, but it fell kindly for Arveladze who skipped past the keeper before tapping the ball home from close range.
There was still time for Stephan Klos to make a marvellous save from a Mckenna header as Hearts fought to the end