The turning point in Saturday's Scottish Premier League clash at the Tulloch Caledonian Stadium came in the 36th minute when Caley midfielder Greg Tansey was controversially sent off by referee Stevie O'Reilly following as he jumped for the ball with Georgios Samaras.
The decision appeared to be harsh but the momentum switched to the visitors who took full advantage.
On the hour Stokes finished a fine move involving James Forrest and Gary Hooper before volleying in a clinching second in the 72nd minute to make it eight goals in eight games for the on-form Irishman.
In terms of a sideshow, all ears were on the travelling support, to whom Neil Lennon had pleaded with not so indulge in the chants which have landed the club in trouble with UEFA and the SPL.
The Parkhead club face a UEFA charge of "illicit chanting" and are under investigation for alleged pro-IRA chants following games against Rennes and Hibernian respectively.
The Celtic fans held up banners before the game which read 'Our music has survived through famine and oppression' and 'Get up, stand up, don't give up your rights'.
There appeared to be little controversy with regards to their song-sheet and the away fans trooped out happy after Celtic ran out comfortable winners in the end.
For today, though, Lennon was more concerned with getting a team together and he made three changes, two enforced, as injuries continued to disrupt his plans.
Midfielder Joe Ledley returned from injury with Badr El-Kaddouri coming in at left-back and Hooper starting in attack.
Midfielder Kris Commons dropped to the bench with injured defenders Cha Du-ri and Thomas Rogne out altogether.
Victor Wanyama stepped back from midfield to partner Daniel Majstorovic at the heart of the Hoops' defence while Chris Hogg returned from suspension to take over from David Proctor in the Caley rearguard.
Neither defence looked particularly impressive in the early stages.
In the 12th minute Stokes left Caley defender Ross Tokely for dead after taking a Samaras flick on at the edge of the box but his curling shot was saved by Caley keeper Ryan Esson.
Parkhead keeper Fraser Forster, for his part, made a decent save from Jonny Hayes' low drive in the 18th minute after the home side exerted a spell of pressure.
It was shaping up to be an intriguing game, most of which was fought in midfield.
Hogg was booked for a trip on Hooper in the 25th minute as the Parkhead striker glided past him just over the halfway line with the Caley defence stretched.
Celtic skipper Beram Kayal then picked up a yellow card for a foul on his Inverness counterpart Richie Foran before Caley defender Josh Meekings' block prevented Stokes squeezing the ball in from eight yards, after Hooper and Forrest had combined well inside the Inverness box.
The game turned when Tansey was shown a straight red by O'Reilly after his challenge with Samaras which left the Greece striker requiring treatment.
It appeared that the decision was harsh and the player was applauded off the park by the home fans, who pilloried O'Reilly as the teams came off at the interval, the referee getting the same treatment at the end of the game.
Two minutes after the restart, Samaras, being booed by the home fans every time he touched the ball, fired wide from the edge of the box.
The visitors were slowly asserting themselves and it was with a clever move that Stokes put them ahead.
Forrest and Hooper worked a one-two at the edge of the Caley box and when the former Scunthorpe striker played the ball across the six yard box Stokes knocked into an empty net.
Moments later, with Caley on the ropes, Esson was forced to tip a shot from Stokes over the bar, after the Irishman was played in by Kayal.
Lennon replaced El-Kaddouri with Paddy McCourt with a view to the Northern Ireland international producing a bit of magic to clinch the points.
However, in the 72nd minute, it was who Stokes sealed the win with a fine volley which flew past Esson and into the far corner after Forrest's shot was blocked by Meekings.
There was shout for a Caley penalty when Foran tumbled in the box following a challenge by Ledley but O'Reilly was unimpressed.
Commons replaced Forrest with 10 minutes remaining and volleyed over the bar moments later from 12 yards but the game was effectively finished by then.