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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1. Allan McGregor - 8
Important saves with the scores level either side of the half. Reacted really well to Bruce Anderson getting a change in the opening 45. A brilliant save right at the end to deny Anderson but couldn't quite keep out Callachan's follow up. Photo: Rob Casey - SNS Group
2. James Tavernier - 3
For his standards a very poor outing. Pinned back by Scott McMann and was far too soft in a challenge which led to a good Accies chance. Photo: Alan Harvey - SNS Group
3. Borna Barisic - 5
Was given a tough time by ex-Rangers man Lee Hodson but became more of an attacking threat in the second half with some dangerous crosses before supplying the opening goal with a superb low cross along the corridor of uncertainty. Didn't react quick enough to Anderson's head late on. Photo: SNS Group
4. Filip Helander - 4
Took a yellow for the team with a barge on Jamie Hamilton in a dangerous position. Ran away from Anderson to allow the striker a free header in the buildup to the equaliser. An incredibly messy afternoon defensively for Rangers. Photo: Alan Harvey - SNS Group