Stokes lofted a free-kick from 22 yards over the United defensive wall and watched the ball ricochet from the left post to the right behind Rado Cierzniak.
Celtic almost opened the scoring on three minutes when central defender Virgil van Dijk carried the ball from the halfway line past three United players before shooting just over the bar from eight yards.
Another summer recruit from Holland, Derk Boerrigter made an impression as he glided past Keith Watson before his cross from the left was headed cleared to the edge of the box where Stokes controlled the ball on his chest and volleyed inches past the post.
Two minutes later van Dijk returned another United clearance past the other post before the hosts finally started to settle into the game.
John Rankin slipped a weighted pass to Stuart Armstrong and his centre was met by David Goodwillie, whose downward header was clutched by the diving Fraser Forster.
The Celtic keeper was also equal to a free-kick from Nadir Ciftci shortly after that when he got over to his right post to push the ball wide.
The unsighted Cierzniak did well to smother a low drive from Kris Commons just after the break but the Hoops suffered a blow when Mikael Lustig was carried off with a serious leg injury after a reckless challenge from Gavin Gunning.
Commons sent a late drive just wide after a Stokes bust into the penalty area resulted in the ball breaking to the diminutive midfielder.
But a minute later Stokes was brought down just outside the box as he beavered towards goal, and from the resulting set-piece the Irishman settled the match.