In the 15th minute of a one-sided first-half peppered by Hoops penalty appeals, none of which were given, midfielder Wanyama opened the scoring at the second attempt following a Charlie Mulgrew corner.
Saints showed resilience if nothing else as they withstood a constant Celtic procession towards their goal but seven minutes from time they succumbed again when former Scunthorpe forward Hooper struck from close range, following another Mulgrew corner.
The Buddies' last victory at Celtic Park was in 1990 and since taking over the St Mirren hotseat in 2010 Danny Lennon has failed to manage a point or even a goal against the champions and earlier in the season the Hoops strolled to a 5-0 victory in Paisley.
Thus, there was no surprise that Celtic emerged victors but it should have been a more convincing scoreline.
The Parkhead club will discover in Thursday's Champions League draw who they will face in the last-16 of the competition and they will certainly have to be more ruthless if they are to progress further.
Celtic manager Neil Lennon had called it right when he brought Wanyama and Hooper back in to the side for Emilio Izaguirre and Lassad Nouioui who both dropped to the bench.
Saints boss Danny Lennon also made two changes with midfielder Jon Robertson in for suspended stopper Lee Mair and wideman Dougie Imrie replacing striker Lewis Guy who started as substitute.
Celtic started in determined mood and in the fifth minute, following a Mulgrew corner, there was a penalty appeal amid Wanyama's header and Efe Ambrose's subsequent shot but referee Calum Murray ignored the pleas, perhaps blinded by the sheer number of Saints defenders in the box.
The official took more stick from the Hoops fans when he ignored a further penalty claim when it looked like an Adam Matthews cross from the byline might have hit a Buddies arm and also when he judged Saints skipper Jim Goodwin and defender Paul Dummett had not sandwiched Hooper in the box.
However, moments later that was all forgotten when Wanyama knocked the ball in from close range after his header from a trademark Mulgrew corner had been spilled by Saints keeper Craig Samson.
In the 26th minute, as the home side continued to monopolise possession, striker Georgios Samaras sent a shot from the edge of the box wide of the far post, before the Greek's low drive from 25 yards moments later drew a decent save from Samson.
With the beleaguered Buddies hanging on, but only just, Ambrose flashed a drive over the bar following yet another Mulgrew corner.
At first glance. the interval respite looked to have revitalised the visitors.
With three minutes played in the second-half midfielder Kenny McLean combined with Robertson before sending a drive from the edge of the box over the bar.
However, Celtic should have doubled their lead in the 51st minute when Samaras' cross from the by-line to the back post allowed Hooper to set up Scott Brown, whose point-blank header was blocked by Samson, with the Hoops skipper taking a bang in the face for his troubles.
The home fans were growing increasingly irritated by Celtic's apparent determination to walk the ball into the net.
Just after the hour-mark, Wanyama, perhaps sensing the mood of the crowd, tried his luck with a 30-yard drive which bounced off Samson but away to safety, before Celtic defender Mikael Lustig headed a Mulgrew corner off the bar, with the Paisley side surviving again.
Despite Celtic's reticence in front of goal the visitors still looked unlikely to level but the Celtic support held its breath during a rare away break in the 66th minute when midfielder John McGinn's left-footed drive had keeper Fraser Forster scrambling down to his left to save.
The home side kept pressing for the second goal and in the 79th minute, after Goodwin was booked for a foul on Hooper 30 yards from goal, Mulgrew sent his curling free-kick over the wall but just past the post.
However, Hooper made sure of the points when he was in the right place to flick in after Mulgrew's corner had landed at his feet a couple of yards out after coming off Marc McAusland.
There was still time for Samson to make another save from Hooper down at his right-hand post but by that time the destination of the points were more than certain.
- Sports & Recreation
- Charlie Mulgrew
- Danny Lennon