Bobby Mann had a half-chance on 17 minutes when Scott Robertson's curling cross came his way, but the big defender couldn't get much power on his header and Raymond Jellema saved.
Paul Dixon was unlucky midway through the first half when Strong's flick from Gavin Swankie's cross fell nicely for him, but his powerful left-foot shot from ten yards rattled the crossbar and was cleared.
Hamilton took a surprise lead on 27 minutes when Derek Fleming's cross from the left was knocked on by Richard Offiong and Paul McLeod nipped in at the back post to head home from close range.
Andy McLaren headed over from an awkward angle after good wing play by Swankie on 38 minutes and, a minute later, a fine save by Jellema denied McLaren what looked like the equaliser.
The home team did equalise on 55 minutes when Strong knocked the ball into the net after Hamilton had failed to clear a Swankie corner.
James McArthur should have regained Hamilton's lead with a quarter of an hour to go, but fired over the crossbar when unmarked six yards out.
McLaren almost grabbed the winner in the final minute but his goal-bound shot was cleared by the visiting defence.