Hearts withstood much Rangers pressure to leave Ibrox with a point and remain five points behind the Glasgow side in the race for second spot in the SPL.
Charlie Adam missed a good chance for Rangers
Rangers captain Barry Ferguson had the ball in the net after 77 minutes but was correctly ruled offside.
Hearts goalkeeper Steve Banks saved well from David Weir and Libor Sionko fired wide from close range.
Nacho Novo and Charlie Adam also went close for Rangers, with Hearts creating little up front.
The game started in controversial fashion with goalkeeper Craig Gordon and midfielder Paul Hartley both surprisingly omitted from Hearts' starting line-up.
Ugo Ehiogu was handed his debut in Rangers' defence in place of Karl Svensson, while Sionko returned from injury to oust Chris Burke from the wing berth.
Rangers started the brighter and David Weir could have fired them into an early lead with a close-range effort.
But Banks managed to tip the ball over his crossbar.
Bruno Aguiar curled a 25-yard free-kick over the Rangers wall, but home goalkeeper Allan McGregor dived low to his right to save.
Rangers should have been ahead midway through the first half.
An Adam corner was nodded into the six-yard box by Kris Boyd and the ball broke to Sionko, but the winger somehow managed to prod wide from a few yards.
Barry Ferguson had a 'goal' chopped off for offside
Boyd then squandered a great opportunity when he was dispossessed by Christophe Berra in front of goal before he could shoot.
Long-range efforts from Aguair and Andrew Driver were all that Hearts could offer in the early stages of the second half as Rangers continued to dominate.
Takis Fyssas fouled Alan Hutton on the edge of Hearts' penalty area, but Adam's free-kick was comfortably cleared by the visiting defence.
Adam then saw a drive held by Banks, after being set up for the shot by Ferguson.
Ferguson had the ball in the back of the net with 12 minutes to go - following good play between Novo and substitute Burke - only for Ibrox to erupt in fury when the effort was ruled offside.
Rangers looked by far the team most likely to snatch the win.
But they failed to find the killer touch that would allow them to put even more daylight between themselves and Hearts.
And their advantage over Aberdeen is now just four points.
Rangers: McGregor, Hutton, Ehiogu, Weir, Murray, Sionko (Burke 72), Ferguson, Hemdani, Adam, Boyd (Sebo 67), Novo.
Subs Not Used: Klos, Svensson, Rae, Lennon, Lowing. Booked: Adam.
Hearts: Banks, Karipidis, Zaliukas (Tall 68), Berra, Fyssas, Mikoliunas (Wallace 59), Aguiar, McCann, Driver, Bednar, Velicka (Elliot 81).
Subs Not Used: Kurskis, Brellier, Jankauskas, John Armstrong.
Ref: Charles Richmond