The Irishman cancelled out Darren Maatsen's third-minute stunner with a tap-in on the half hour, and he ensured maximum points when he drilled a low shot past Mark Brown with three minutes remaining.
Ross County formed a guard of honour for the reigning champions before kick-off but they were less charitable once the game kicked off and stunned the hosts on three minutes.
Maatsen was invited inside the area with the ball and he punished some slack defending by unleashing a rasping shot that flew past Fraser Forster.
Maatsen's strike woke the hosts from their slumber and they went on to dominate the remainder of the game, but they found Mark Brown in inspired form, the County goalkeeper producing smart saves to deny Derk Boerrigter and Kris Commons.
But Brown was let down by his defence on 28 minutes when they failed to properly clear Commons' corner. Mikael Lustig's scuffed effort came back off the post and Stokes was on hand to tap home the rebound.
Celtic lost debutant Boerrigter to an ankle injury but they remained on top, with Efe Ambrose blazing over and Brown denying Stokes to ensure the scores remained level at the break.
The game continued in a similar fashion after the interval, Stokes again going close with a volley and Commons crashing a shot off the crossbar as gaps began to appear in County's defence.
Former Celtic player Graham Carey went close with a free header but it was a rare foray forward by County, and Charlie Mulgrew saw a header come back off the post at the other end.
Celtic piled bodies forward late on and it paid off on 87 minutes when Commons found Stokes to the left of goal. He cut inside and fired a low shot past Brown to ensure Celtic got their title defence off to a winning start.