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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9. Ianis Hagi - 5
Saw too much of the ball away from the final third. Has produced plenty of magic moments of late but wasn't the case at Accies. Photo: Alan Harvey - SNS Group
10. Ryan Kent - 5
Was more dangerous in the latter stages but didn't do enough. Photo: Rob Casey - SNS Group
11. Cedric Itten - 6
One of the few, perhaps only, outfield Rangers players to show up well in the first, creating space and openings for team-mates. Had a to battle manfully and fed off scraps. Photo: Craig Foy - SNS Group
12. Ryan Jack - 7
Quality evident from the moment he stepped on to the pitch. Added greater purpose and direction to the team. Photo: Rob Casey - SNS Group