Brian Rice's men were the better side for large spells forcing Allan McGregor into the most amount of saves he has faced in the Premiership this season.
Man of the match McGregor branded the performance rubbish, while Steven Gerrard admitted he was relieved to be going away with a point because his team didn't deserve it.
Rangers got ahead through a Brian Easton own goal after a nice move down the left but Accies equalised at the death when Ross Callachan pounced on a rebound from Bruce Anderson's header to squeeze an effort into the net.
How did the Rangers players rate?
Player ratings scale - 10: One of the best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen.
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13. Kemar Roofe - 6
A bit more mobility to Itten but didn't get much in the way of a chance at goal. Photo: Alan Harvey - SNS Group
14. Steven Davis - 6
A brilliant pass to send Barisic free down the left in the build-up for the goal. Allowed Hughes to run off him for the equaliser. Photo: Alan Harvey - SNS Group
15. Scott Wright - 6
Looked positive in his ten or so minutes on the pitch. Picture: SNS Photo: Alan Harvey - SNS Group