Ali Crawford struck four minutes into the second half when he smacked a shot past Craig Gordon after the Celtic defence failed to deal with a Stephen Hendrie cross into the box.
Celtic were stung into life and Kris Commons was denied within 60 seconds when Michael McGovern made a finger-tip save to keep his net bound effort out.
Two minutes later, Hoops defender Jason Denayer had a header cleared off the line as Accies defended resolutely.
The home side felt they had a strong case for a penalty when Aleksandar Tonev appeared to be upended by Grant Gillespie in the box, but a corner was given and the Hamilton player was booked.
Celtic also had a handball shout waved away as Dougie Imrie ran the ball out of play.
But Hamilton had chances to increase their lead as well and Louis Longridge was denied when his shot was deflected inches wide.
Accies then created another chance on the counter-attack when Anthony Andreu curled a shot narrowly wide from the edge of the box.
With 15 minutes remaining substitute Leigh Griffiths sent a volley from an Efe Ambrose cross past the near post.
Tony Stokes then squandered a golden opportunity in the dying minutes when he headed past the target from close range from a Tonev delivery.
In the opening half Hamilton midfielder Daniel Redmond forced Gordon into action with a shot from outside the penalty area.
Stokes put a shot wide at the other end a minute later and also had another attempt saved by McGovern shortly before the break.