St Mirren had squandered a chance to open the scoring through Lewis Guy before two goals in three minutes put the Hoops on top.
Gary Hooper tapped in a 15th minute opener from close range before Efe Ambrose volleyed home in the 18th minute following a fumble from Craig Samson.
Kenyan international Wanyama rifled home a third in the 32nd minute before the midfielder bagged his double with a sensational strike from 30 yards that left the keeper with no chance.
The Hoops took their foot off the pedal in the second half but teenager Tony Watt was still able to head home a late fifth as Celtic cruised to the biggest win of the SPL season.
"They were magnificent, every one of them. They had a great attitude and there was a good tempo to the game," Celtic manager Neil Lennon said.
"We were clinical in front of goal but having said that we had to rely on (keeper) Fraser Forster a couple of times - but we were awesome today."
St Mirren manager Danny Lennon was bitterly disappointed.
"It is a very emotional dressing room for the players and the staff," Lennon admitted.
"I felt we started the game reasonably well and then we gave away poor goals.
"We certainly met a Celtic side on top form and with us being well below par I have no complaints on how the game went."
With one eye on Tuesday's Champions League tie against Barcelona manager Neil Lennon made five changes to his side with Scotland trio Scott Brown, Kris Commons and James Forrest all nursing injuries.
Teenager Watt started only his fourth game for the Hoops and he immediately had a chance but keeper Samson was quick off his line to make a brave block at the striker's feet near the penalty spot.
St Mirren were next to threaten and could have taken the lead when a deep cross from David van Zanten found Guy in behind Celtic defender Efe Ambrose but the striker sent his first-time volley straight at Fraser Forster.
The Buddies were left to rue that missed chance when Celtic went in front in the 15th minute as Hooper scored his 10th goal of the season. Tunisia international Lassad Nouioui drilled a ball across the six-yard box and the English striker knocked the ball past Samson from close range.
The Hoops doubled their advantage just three minutes later when Samson fumbled a Charlie Mulgrew free-kick and Nigerian international Ambrose was on hand to volley in his first Celtic goal.
It was all over for the home side in the 32nd minute when Wanyama made it 3-0 after an Adam Matthews corner came off two St Mirren defenders.
Wanyama then got his second of the match with a spectacular curling strike from 30 yards that flew into the top corner in the 38th minute.
In the second half St Mirren missed a chance to pull a goal back when Graham Carey picked out Steven Thompson for a shot but the striker could only send his shot straight at Forster with Carey sending the rebound high and wide.
Skipper Jim Goodwin then set Thompson up for another chance but he flashed his effort just over.
With four minutes remaining Watt made it 5-0 when he got on the end of substitute Emilio Izaguirre's cross to power a header past Samson from ten yards out.
Source: AFP
Source: AFP