Accies exerted all of the pressure, while Kilmarnock were guilty of far too many stray passes and posed very little attacking threat.
Referee Craig Thomson infuriated the home support in a scrappy opening by booking Frazer Wright for pulling back Offiong, and then failing to speak to the Hamilton striker for a similar offence.
Offiong hooked the ball over the crossbar with his back to goal and Wright made a brilliant headed clearance from McArthur's dangerous cross.
Killie keeper Alan Combe dived at full length to tip wide Canning's deflected effort from the edge of the penalty area.
And Craig Bryson was relieved to see his sliced clearance bounce on to the roof of the net from McGowan's fizzing near-post corner.
James Fowler was having a real off day for the hosts and he almost cost his side dear when he gifted possession to James McCarthy on the halfway line.
The ball was moved on swiftly to Offiong, who saw his attempted chip clawed away by Combe, while McCarthy hit the post with an awkward right-foot shot as he raced in for the rebound.
Accies trio McCarthy, McGowan, Jordan McMillan and Killie midfielder Manuel Pascali all followed Wright into Thomson's book before the interval as the referee waved his yellow card with alarming regularity.
Thomson did nothing to improve his popularity with the home fans when he signalled a goal for Accies in the opening minute of the second half. However, there was no dubiety about the award.
A slick move from the re-start, saw the visitors win a corner and, when Brian Easton flicked on McGowan's delivery, Offiong got a touch to nudge the ball over the line, despite a cluster of defenders trying to keep it out.
A poor headed clearance from Simon Ford set McGowan up for an impressive volley which was well saved by Combe and when the loose ball came back to the Accies man it was blazed high over the crossbar.
It took Kilmarnock 67 minutes to register their first attack of note when Danny Invincibile let fly from 25 yards and his shot whizzed narrowly wide.
McGowan replied with a fierce shot across goal after some slack defending from Gavin Skelton, while Combe had to make a smart save from Mark McLaughlin's nimble turn in the penalty box.
The hosts pinned Hamilton back for much of the final quarter but Tomas Cerny's only moment of concern came when his Canning dummied a poor cross from Mehdi Taouil, and the visiting keeper got down well to hold the ball.
Sandy's Match Pic's are HERE
