The Republic of Ireland striker struck twice (60,72) in 12 minutes in the second period after Greg Tansey was harshly red carded for the illegal use of an elbow in challenging Georgios Samaras in the air 10 minutes before the half-time.
The importance of that result was emphasised later in the afternoon when Rangers were held to a 0-0 draw by St Johnstone at Ibrox with the Perth side producing an outstanding display under their new manager Steve Lomas to earn a merited point.
Celtic have one game in hand on Rangers, and will close the gap to seven points if they overcome Dunfermline Athletic on Wednesday night at Celtic Park.
Celtic made the breakthrough when Gary Hooper and James Forrest combined beautifully on the edge of the home area before Hooper squared for Stokes to tap the ball into the unguarded net.
The visitors were always in control from that point onwards and added a second when Stokes thumped a powerful volley low into the corner of the net after Forrest's initial shot had broke kindly for the his team-mate to apply the finish with a powerful volley.
Celtic goalkeeper Fraser Forster dived to make a fine stop from Johnny Hayes on 19 minutes while Josh Meekings did superbly well to clear the ball as Stokes seemed set to net the opening goal on 31 minutes.
The game changed when referee Steve O'Reilly decided Tansey had elbowed Samaras late off the ball. It was never a red card, but Celtic only benefited from the one-man advanateg when they introduced Ki Sung-Yueng for Samaras on 57 minutes.
Joe Ledley was shoved further forward as Celtic suddenly began to give a tiring Inverness side serious problems in the last 30 minutes.
The win gives Neil Lennon's side a measure of revenge after they lost 3-2 to Inverness in losing the SPL title by a point to last term.
Rangers suffered another post-international break slump when they were held to a goalless draw by St Johnstone in their SPL clash at Ibrox.
Neither side were able to find the back of the net, with the stalemate allowing Celtic to close the gap on the SPL leaders to 10 points .
Ally McCoist's men were therefore forced to share the points with St Mirren in front of a frustrated home crowd upon their return to league business following the last international break.
Rangers made three changes from their last outing against Dundee United. Kirk Broadfoot, Alejandro Bedoya and Kyle Lafferty all started at Ibrox, with Sasa Papac, Lee Wallace and Kyle Bartley all sidelined through injury.
For new Saints boss Steve Lomas, the visit to Glasgow provided the opportunity to start his new job on a high as he took charge of team affairs for the first time after replacing Derek McInnes at the helm.
Rangers had the first real chance of the game when Broadfoot whipped a cross into the box for Nikica Jelavic and he connected with a diving header that fell just past the post. Steven Davis then teed up Jelavic with a cut-back in front of goal but this time the Croatian striker was denied by a timely block from Frazer Wright to keep the scoreline level.
Rangers looked the more likely of the two teams to find the back of the net and pushed forward in search of the opener with half-time approaching. Steven Whittaker burst down the right flank before trying to pick out Lafferty but goalkeeper Peter Enckelman was able to gather at the near post before the forward could connect.
St Johnstone started the second half well and one-time Rangers target Murray Davidson saw his effort flash just past the upright a couple of minutes after the restart.
Davidson was threatening again when he threw himself in front of a Chris Millar cut-back only to see his header touched just over the crossbar by a full-stretch Allan McGregor.
Rangers had the chance to pile on the pressure when Lafferty won a free-kick 25 yards out. He squeezed a low effort through the Saints defence before Bedoya tried to force over the line but Enckelman managed to smother.
Motherwell clinched a testing 2-1 victory over Aberdeen in their clash at Pittodrie with goals from Michael Higdon and Omar Daley securing all three points.
Scott Vernon equalised in the 10th minute for the hosts to cancel out Higdon's opener, but Daley netted what proved to be the winner in the 53rd minute.
St Mirren were also victorious as they defeated Dunfermline 2-1 at St Mirren Park courtesy of goals from Kenny McLean and Nigel Hasselbaink.
McLean and Hasselbaink gave the hosts a two-goal lead, and substitute Joe Cardle's goal just after the hour mark was insufficient for Dunfermline.
Hearts suffered a setback in their match against Tannadice Park against Dundee United to drop to sixth place in the SPL table.
A clinical strike in the 24th minute from Scott Robertson was enough to seal all three points for the hosts at Hearts' expense.
Meanwhile, Hibernian salvaged a point from their home encounter with Kilmarnock in a 1-1 draw at Easter Road.
Manuel Pascali opened the scoring in the 37th minute for Kilmarnock, but the hosts hit back through substitute Leigh Griffiths to share the spoils.