A point looked the most likely outcome on a freezing cold Sunday afternoon at New Douglas Park until Hartley combined with Scott Brown to devastating effect, rifling the ball past helpless Tomas Cerny.
Accies nearly took the lead after just eight minutes when captain Alex Neil and James McArthur linked up well on the right.
The ball fell to Richard Offiong but the English striker curled a fierce effort just over.
But the Lanarkshire side took the lead seven minutes later. Trent McClenahan made an excellent run down the right before swinging in a superb cross for Offiong to bullet past Mark Brown with a close-range diving header.
But, as is customary for Hamilton Accies, they conceded an equaliser just before half-time when Martin Canning was judged to have hauled down Cillian Sheridan in the box.
On this occasion, referee Steve Conroy made the wrong decision as replays seem to show the foul taking place outside the box.
Nevertheless, Canning was handed a straight red card and Shunsuke Nakamura stepped up to clinically bury the penalty, although Cerny wasn't far away.
Hamilton had gone desperately close to grabbing a second before Nakamura's strike as Brian Easton's corner was met well by Offiong, but the ball was headed off the line.
At the other end, Andreas Hinkel's ferocious drive was well parried round the right post by Cerny.
But the penalty and sending off were the turning point in this game, although credit to Hamilton for not giving up against the league leaders.
It was difficult for the second half to live up to that excitement, although Celtic were perhaps fortunate not to concede a penalty after 53 minutes after Stephen McManus appeared to foul James McCarthy in the box.
Cerny kept Hamilton in the game with five minutes left when he produced a simply breath-taking save to parry sub Georgios Samaras' close-range diving header.
But with three minutes left, Hartley played a neat one-two with Brown on the edge of the box before rifling a stunning half-volley past Cerny.