Superior Accies bossed the first period but were stunned seconds before the interval when the Motherwell striker knocked the ball in from 12 yards after Hamilton keeper Tomas Cerny had parried a Steven Hammell cross.
Motherwell keeper Graeme Smith, who had pulled off a great save from Kenny Deuchar early in the game, made
another fine block from Alex Neil in the second half as Accies tried everything to get back level.
However, the home side held on - grimly at times - to extend their unbeaten run to nine games and take them closer to a coveted top-six spot.
It was tough luck on Billy Reid's side who deserved at least a point for their efforts in what was a game unsurprisingly lacking in finesse on the terrible Fir Park surface.
Motherwell manager Mark McGhee criticised the Well supporters in his programme notes, claiming they had been "out of order" in their barracking of the players during their Homecoming Scottish Cup draw with St Mirren last week which stretched their unbeaten run to eight games since losing to Accies in December.
It was not the first time the Fir Park boss has hit out at the supporters this season but his mood may not have been helped by the fact that the Lanarkshire club had been handed a suspended £20,000 fine by the SPL following problems with their undersoil heating which caused the game against Hearts in December to be postponed.
Hamilton took to the much-maligned Fir Park playing surface in confident mood with young player of the month James McCarthy, in midfield, and player of the month, Tomas Cerny, in goal.
The visitors threatened first in the fourth minute when James McArthur's 25-yard drive was re-directed by the head of Deuchar, leaving Smith to change direction before brilliantly pushing the ball round the post for a corner.
From Neil's corner, Mark McLaughlin's header was again well saved by Smith before the referee Dougie McDonald blew for an infringement as Simon Mensing forced the ball over the line.
Moments later, Neil despatched a volley from 25 yards which cleared the far post by a matter of inches.
In the 17th minute Motherwell eventually surfaced as an attacking threat when playmaker Stephen Hughes took a Clarkson pass and drove an angled-drive from 14 yards past the far post with Cillian Sheridan arriving too late to capitalise.
That should have been the sign for Motherwell to increase their output but in the 25th minute skipper Stephen Craigan got himself unnecessarily in trouble from a long punt from Trent McClenahan, allowing McCarthy in at the edge of the box.
However, the Republic of Ireland Under-21 player snatched at the volley and the ball sailed over the bar.
Accies had the edge but in the final seconds of the half, they were undone when Hammell drove in to the Hamilton box and fired in a cross-shot which Cerny parried under pressure from Sheridan.
With the Accies defence momentarily in disarray, Clarkson was on hand to bundle the ball over the line.
The visitors had every right to be stunned as they left the field at the break and Motherwell, unsurprisingly, emerged for the second half buoyed by their good fortune.
McArthur let his frustrations boil over in the 50th minute when he was booked, deservedly, for a late challenge on Motherwell's hardy midfielder Maros Klimpl.
It was heating up nicely and Fir Park defender Paul Quinn was then booked for dissent.
Moments later, Smith was forced in to another fantastic save, this time from Neil's powerful volley from 14 yard out with Quinn tidying up the loose ball.
From McCarthy's corner, the unmarked Deuchar headed over at the near post but Accies stepped up their quest for the equaliser on a rapidly deteriorating playing surface.
Accies continued to push forward but 10 minutes from the end they survived what looked like a decent penalty claim when Cerny clashed with Quinn inside the six-yard box.
Referee McDonald had a good look but took no action as the Fir Park right-back pulled himself off the floor.
Hamilton kept going until the end of the four minutes of added time but could not prevent their first defeat in seven games.