After setting up a 44th-minute opener for Gary Hooper, who was returning from an ankle injury, Stokes tucked in a 50th-minute penalty following a foul by Lewis Stevenson.
Stokes, who moved to Celtic last August after helping Hibs to fourth place last season, skilfully netted his second after 64 minutes to confirm a 12th league loss of the season for his former club.
A 15th win of the campaign consolidated Celtic's place at the top of the SPL and saw the Bhoys end a difficult week on a high.
Neil Lennon's men now have 49 points, but Rangers have three games in hand - four if you include this afternoon's clash with bottom club Hamilton.
Manager Lennon is appealing a six-match touchline ban imposed this week after he was sent to the stand by Saturday's referee Craig Thomson during a defeat by Hearts in November.
The ban did not prevent Lennon from branding the performance of referee Willie Collum as "not good enough" in the 1-1 draw at Hamilton on Wednesday night.
Collum was today in close proximity to Lennon - he was the fourth official.
Lennon was up against one of his former managers in Colin Calderwood, who was the Celtic boss' manager at Nottingham Forest and was seeking to improve a record of two wins in 12 games in charge at Easter Road.
After drawing 0-0 with Irn-Bru Second Division Ayr in the Scottish Cup last weekend, Hibs responded with a strong start against the SPL leaders.
David Wotherspoon headed wide from Stevenson's cross in the opening minute after the full-back had overlapped on the left before Derek Riordan hit a 30-yard free-kick over.
Celtic's first chance came when Emilio Izaguirre shot tamely at Mark Brown before Daniel Majstorovic inexplicably fluffed a free header from close range following Mark Wilson's free-kick.
The defender was played onside by Hibs' defence, but the ball bounced off his shoulder and head to go off target, much to Lennon's frustration.
Brown then saved with an outstretched leg from Hooper, who was played through by an incisive ball from Beram Kayal, a player earlier booked for fouling Ian Murray.
Hooper needed no second invitation, though, when netting moments later.
Stokes did well on the left of the area to feed his strike partner, whose first touch helped him evade marker Paul Hanlon and he coolly slotted in. It was his 12th goal of the season.
Early in the second half Majstorovic diverted Izaguirre's corner towards goal, with the ball held by Brown.
But Stevenson then scythed down Stokes a yard inside the penalty area after 49 minutes, referee Thomson pointing to the spot without hesitation.
Stokes stepped up and passed the ball straight down the middle of the goal to net for the 11th time since leaving Edinburgh for Glasgow last August.
Stokes shot off target from Paddy McCourt's pass after 56 minutes before Danny Galbraith had an effort ruled out for offside.
Majstorovic cleared off the line after Wotherspoon and Riordan combined before Wilson fouled Merouane Zemmama on the edge of the area. The Moroccan's free-kick was deflected wide.
McCourt then ran at the Hibs defence and made space for a shot, which Brown scrambled around the post.
From the resulting corner Stokes netted his second.
The striker brought down Izaguirre's cross and lofted the ball into the top corner beyond Brown.
It was yet another reminder of how much Hibs have missed his ability in a run which sees them perilously close to the relegation zone.
And he could have had a hat-trick after Francis Dickoh's header from Zemmama's corner was easily held by Fraser Forster.
The goalkeeper launched a counter attack and Stokes, played onside by the Hibs defence, went through one on one with Brown and lofted the ball over the goalkeeper, but Dickoh recovered to head off the line.
Freddie Ljungberg, on for Hooper, had a cross blocked in the area by Murray but Celtic's appeals for handball were ignored.
Forster tipped Duffy's flick from Galbraith's cross on to the bar to deny Hibs as Celtic banked more points, returning the pressure on Rangers.