When Rennes skipper Kader Mangane headed the French side into the lead from a Julien Feret corner with less than two minutes on the clock it looked like being a long night for Neil Lennon's men.
However, in a spirited comeback James Forrest's drive on the half-hour mark was parried by Rennes keeper Benoit Costil to the feet of Stokes who knocked into the net from close range.
Two minutes before the break the Irishman grabbed his second with a drive after racing onto a Georgios Samaras header and in the 81st minute the Greece striker set up Hooper to score number three as the visitors finished with 10 men after star midfielder Yann M'Vila was sent off after picking up two yellow cards.
Celtic go within two points of the top of Group I with two games remaining but more importantly any notion that team spirit was lacking was blown away and they will go to Fir Park on Sunday for their crunch Scottish Premier League clash with Motherwell full of confidence and looking to claw back the 12-point deficit on leaders Rangers.
Lennon was again forced to ring the changes with six in total from the side which drew 0-0 with Hibernian at the weekend.
Before the game Celtic announced that right-back Mark Wilson would be out for three months following knee surgery but also out through injury were Charlie Mulgrew and Joe Ledley while Ki Sung-yueng was ill, Thomas Rogne was not registered and thus unavailable and Hooper was dropped to the bench.
In came Cha Du-ri, Glenn Loovens and Daniel Majstorovic into a reshuffled back four, while there were starts for Paddy McCourt, Victor Wanyama and Samaras.
However, there was less than two minutes gone when the visitors took the lead following the first corner of the game.
Feret's driven cross from the right was met by Mangane who bulleted his header into the net at the far post to stun the Hoops fans.
Against a slick-moving French side Celtic could not get into gear, although wide-man Forrest was showing glimpses down the right-hand side.
There appeared to be no signs of an equaliser but out of the blue, Stokes found himself in the right place to draw the home side level.
Forrest picked up a loose ball in the middle of the park and drove forward before unleashing a low drive which Costil could only parry straight to the Irishman who had the easiest of tasks in knocking into the net.
The goal revitalised Celtic and the tempo of their play increased but there were still signs of sloppiness which allowed Rennes to cause alarm.
However, two minutes from the break, Stokes struck again.
Keeper Fraser Forster's long punt was headed on by Samaras and as Mangane stumbled, Stokes raced into the box before sending a left-footed shot into the far corner to put Celtic ahead.
It was a remarkable turnaround for the home side who were cheered up the tunnel.
There were more injury woes for Lennon to contend with at the interval.
Loovens had picked up an injury which meant under-19 defender Marcus Fraser came on to make his competitive debut.
Celtic made a more assured start to the second half with McCourt burrowing his way into the Rennes box in the 50th minute only to run into traffic.
The visitors dominated possession but Celtic dropped back to repel the French attacks although on the hour mark substitute Victor Montano, on for Abdoulrazak Boukhari, headed Feret's free-kick over the bar from close range when he ought to have at least hit the target.
In the 66th minute Kris Commons replaced McCourt and was given a huge cheer by the Celtic fans.
The game was much more even now with Rennes lacking the confidence displayed in the first half as the Celtic players chased and harried them all over the pitch.
As the minutes ticked away, Celtic dropped deeper and Forster made two good saves from substitute Youssouf Hadji, on for Feret, first from a shot from the edge of the box, the second from a header at the back post.
In the 78th minute Hooper came on for Forrest and three minutes later, in a Celtic breakaway, he knocked in a Samaras pass to secure the points.
Then, with five minutes remaining, M'Vila, booked in the first-half for a foul on Forrest, was sent off by referee Bruno Paixao after a foul on Commons as Celtic ran out comfortable winners.