The result means Motherwell are now favourites to take place in the relegation play-off against a Championship opponent at the end of the season.
Jason Scotland opened the scoring on 21 minutes before Ali Crawford struck in the early stages of the second half as suspended player-manager Canning watched the team win for the first time in 14 attempts.
Accies created the first chance six minutes in when the ball broke to Grant Gillespie just outside the penalty area and as he strode into the box the slightly off-balance midfielder sliced his shot wide of the target.
The visitors responded when Scott McDonald slipped a pass in front of Gareth Ainsworth who crashed a shot through a defender’s legs forcing Michael McGovern to palm the ball across the six yard box where it was headed clear by Gillespie.
The breakthrough came when Crawford pounced on some slack play from Lee Erwin just inside the Motherwell half and threaded a pass in front of Scotland who had drifted between two defenders to shoot into the goalkeeper’s bottom-right corner.
Four minutes later Accies defender Michael Devlin collided with McDonald inside the D and Erwin took the ball in his stride to crash a first-time drive off the upright from 16 yards.
Devlin then got up at the near post to meet a corner from Crawford and his glancing effort was blocked by the unaware Marvin Johnson, before the pair combined again from the resulting flag-kick when the Accies defender sent a dipping header against the bar.
At the other end Johnson drifted into the left side of the Hamilton box on to a lofted pass from McDonald and stepped inside Darren Lyon before crashing his shot off the front of the crossbar.
Shortly before the break Erwin used his strength to win the ball just inside his own half and slip a pass on to McDonald who stepped past Gillespie and returned a reverse delivery to his fellow forward, but he was denied by McGovern’s leg before Devlin tidied up.
Seconds after the interval Hendrie raced down the Accies left flank and tried to catch out George Long at his near post but the Motherwell ‘keeper got across the keep save the shot.
Erwin was inches away from connecting with an Ainsworth free-kick as he came sliding in at the back post, with a slight deflection from Scotland aiding the Accies cause.
It was a turning point as three minutes later Dougie Imrie produced a burst of pace in the middle of the park and played a weighted pass in front of Crawford (52), who produced a similar finish to the first goal by shooting across Long into the bottom corner.
Motherwell continued to battle though and Dominic Thomas came close on 69 minutes when his low shot from the edge of the penalty area went through a the legs of a defender and shaved McGovern’s left post.
And Hamilton survived a couple of scares when Ainsworth delivered another free-kick in from the Motherwell left wing and substitute John Sutton (83) glanced his header wide of the far post and the advancing McGovern kept out an Erwin shot with his legs after Stephen Pearson had sent the winger clear.