Dumbarton got off to a flyer through Gregor Buchanan’s third-minute opener but Dominique Malonga equalised 11 minutes later in a half largely dominated by the away side.
But when Kevin Cawley was fouled early in the second half, Gibson made no mistake with a beautifully executed free-kick to hand Dumbarton the points.
Meanwhile an inspired performance from Mark Stewart helped Raith Rovers claim a convincing 3-0 opening-weekend win over Livingston.
Stewart put the home side in front after eight minutes before winning a penalty 11 minutes prior to the interval. Ryan McCord’s textbook spot-kick doubled the home side’s advantage before Mitchel Megginson struck in the last minute to put the gloss on the win.
Elsewhere, Queen of the South raced into a three-goal half-time lead after Derek Lyle’s fifth minute opener against Alloa Athletic was followed up by a double from Iain Russell.
New signing Michael Chopra came on at half-time and made an instant impact for the visitors, feeding Iain Flannigan who smashed home from outside the area within three minutes of the restart.
But Alloa were unable to get within sight of the home side as Queen of the South ran out comfortable 3-1 winners.
The day’s other Scottish Championship game saw Greenock Morton draw 1-1 with Falkirk after Peter MacDonald’s close-range header on the hour mark cancelled out Paul Watson’s first-half strike for the visitors.