The visitors broke the deadlock shortly before half time when a Commons pass fell to Adam Matthews on the edge of the box, leaving the Welsh international to hit it first time, rooting McGovern to the spot.
Scott Brown had a chance to double their advantage just before the interval, but his curling effort flew well high of the crossbar.
Dougie Imrie tried to get Hamilton back into contention with a low effort, trying to pick out the bottom right, but Gordon spotted the danger for the visitors.
Callum McGregor had a chance to put the win beyond doubt inside the final 15 minutes as he tried to pick out the top left corner, but McGovern punched the ball away before Virgil van Dijk blasted the rebound wide.
Hamilton kept pushing late into the match as Ali Crawford tried to give the home side some late hope with a long-range effort, but Gordon watched it all the way to make a comfortable catch.
The result leaves Celtic second in the table, while Hamilton stay fifth.