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.
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 Lennon also made two changes with midfielder Jon Robertson in for suspended stopper Lee Mair and wide-man 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.
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 Mulgrew sent a 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.