The Ibrox men seemed on course for a rout when they went two up after only 20 minutes but it took them until the 70th minute to close out Hearts, who battled hard but were not in the same class as Rangers.
Dick Advocaat even had the luxury of easing Neil McCann and Stephen Hughes back into the action from the bench which augurs well with the visit of Hibs due on Wednesday.
Rangers took just six minutes to stamp their authority on the match when Ronald de Boer gave them the lead and the simplicity of the strike was indicative of the Ibrox side’s dominance.
It was Russell Latapy who created the opportunity and there was even more to come from him later in the match as he relished a rare starting slot due to the injury situation.
The former Hibs star cut across the edge of the Hearts penalty box and played a neat pass through to de Boer who was in the clear. The Hearts defenders were claiming for offside but the Dutchman was onside and tucked the ball past Antti Niemi with his right foot.
It was everything Rangers deserved as they started strongly, stretching Hearts down the left side in particular where Shota Arveladze gave Kevin McKenna a really torrid time.
Even although Rangers had regular wing backs Fernando Ricksen and Arthur Numan in central midfield roles and both Scott Wilson and Tony Vidmar were also in the side for rare starts they were infinitely too strong for the Edinburgh side.
They went two up in 20 minutes and it was a quite superb goal as Hearts were ripped apart by a move which started just outside Rangers’ box.
Vidmar spotted Claudio Caniggia in midfield and picked him out perfectly to catch the Hearts defenders on their heels. Caniggia’s control was excellent and he was quick to feed de Boer on the left side.
Hearts were still trying to regroup when de Boer drove the ball across the face of the box and Latapy clipped a delightful left foot shot which took a slight deflection before nestling in the left corner of Niemi’s net.
Rangers were all over the Edinburgh men at this stage and they came desperately close to adding to their lead. In 23 minutes Caniggia twisted and turned on the edge of the box before playing in Arveladze whose first time shot fizzed over the bar.
The a minute later Hearts were exposed again when Amoruso brilliantly picked out de Boer, who had cleverly remained onside. The Dutchman raced forward and cut onto his left foot to try and find the top left corner but the ball flew just over.
Hearts, though, were given some encouragement in 32 minutes when Thomas Flogel’s cross was poorly defended by Vidmar, who headed the ball straight to Tommi Gronlund whose right foot shot flew just over the top.
They were given even more encouragement in 39 minutes when they managed to pull a goal back. Disappointingly for Rangers it was from a set piece and they have conceded a few goals in this manner this season.
Hearts won a freekick in a left central area and Andy Webster had a crack. Sadly for Stefan Klos it took a deflection and wrong-footed the German to give Hearts a lifeline.
Rangers took a bit of time to regain their grip on the game as Hearts enjoyed some decent possession in the early moments of the second half. Klos had to look lively to stop Kevin McKenna’s freekick in 58 minutes and then Amoruso made an absolutely vital challenge on Flogel in 69 minutes just as the Austrian was shaping to shoot.
It was a timely intervention because a minute later Rangers made the game and the points safe with a third goal and it was another strike for Shota Arveladze.
Hearts were caught on the break by Vidmar who burst forward before releasing Caniggia. The veteran striker played a neat one-two with Arveladze and seemed certain to score but Niemi blocked his effort.
Shota, however, followed up to stroke home his eighth goal of the season. Rangers took some time to close the game out but it was a thoroughly deserved win.
Arveladze might have made it an even more emphatic win when he was sent clear in injury time but he shot over the top but it did not really matter in the grand scheme of things.
RANGERS: Klos; Ross, Wilson, Amoruso, Vidmar; Ricksen, Latapy, Numan; Caniggia (McCann 73), de Boer (Hughes 70), Arveladze. Subs not used – Christiansen, Moore, Flo.
Bookings:
HEARTS: Niemi; McKenna (Boyack 74), Pressley, Webster; Maybury, Flogel, Gronlund (Kirk 84), Fulton (Wales 74), Mahe; Fuiller, Symmons. Subs not used – McKenzie, McCann.
Bookings:
Ref: Kevin Toner.
Att: 47,891
Man of the match: Maurice Ross
Moment of the match: Ross’s crunching challenge on Stephane Mahe in front of the Broomloan Stand.