The midfielder and striker got the goals to help the league leaders get back to winning ways at Celtic Park with a comfortable victory against the relegation threatened Buddies
The Paisley side now find themselves entrenched in a relegation battle after only being able to claim three points in one of their last 10 league games.
The home side made two changes from the side that defeated Arbroath in the Scottish Cup, with Wanyama and Hooper coming in for Emilio Izaguirre and Lassad Nouioui.
While St Mirren also made two changes from the side that drew at home to St Johnstone, with both Lee Mair and Lewis Guy dropping out to be replaced by Jon Robertson and Dougie Imrie.
Hoops boss Neil Lennon was angry at referee Callum Murray as he failed to award a penalty to the league leaders as Hooper had appeared to have been pushed by on-loan Newcastle defender Paul Dummett, as the English striker raced in on goal.
They did eventually take the lead as Wanyama got on the end of a Charlie Mulgrew corner from the left wing and after failing with his first attempt, the Kenyan midfielder powered the ball past Craig Samson in the St Mirren goal.
The SPL champions continued to pepper the St Mirren goal for the reminder of the first half, with Adam Matthews crossing from the right in search of Mulgrew, but before he could get to the ball David Van Zanten got in the way to clear for a corner.
It was like a training match for the Hoops, as they continued to pressure the Paisley outfit, with Georgios Samaras the next up to try his luck with a volley from the edge of the area, but his strike went just wide.
The Greek then had another attempt before the break, after stealing possession and playing a one-two with Wanyama, before unleashing a strike from the edge of the area, but Samson got down well to clear the danger.
Celtic should have doubled their lead as Samaras crossed from the left to Hooper at the back post and he knocked it back into the danger area for Brown, but his header from two yards out hit the midriff of Samson and was eventually cleared.
The onslaught of the St Mirren goal continued as Samaras put in a cross from the left, which Samson spilled into the path of Brown, but his chance was blocked as he tried to find the net through a wall of St Mirren defenders.
Next up for the Hoops was Mikael Lustig as the Swedish defender got onto a corner from the right by Mulgrew, but his headed attempt cannoned off the junction of the post and bar and then went away from danger.
The three points were sealed late on, once again from a corner, as Mulgrew crossed from the left and after St Mirren failed to clear, Hooper turned and slotted the ball home to claim the victory.