The home side dominated for large spells of the game but could not find a goal until injury time when Junior Morias netted from close range.
St Mirren made just one change from the team that defeated Ross County. In came captain Stephen McGinn for his 200th club appearance, with Danny Mullen dropping to the bench. Hibs, in contrast, were unchanged for a third match in a row as new manager Jack Ross returned to Paisley.
It was the home side who created the first chance after four minutes. Kyle Magennis squared the ball for Ilkay Durmus but the Turk's wild effort went well wide of the goal.
Hibs responded with their first opening. Joe Newell's hook back into the box was a dangerous one but referee Alan Newlands was quick to blow for a foul on goalkeeper Vaclav Hladky.
Magennis should have then done better with the first real chance of the game. Calum Waters' cross from the left was perfect but the midfielder could not get his header on target from six yards.
The home side paid for those missed chances when Hibs went in front after 28 minutes. Jason Naismith's cross from the right was met by Doidge and he scored his sixth goal in three matches with the aid of a deflection.
St Mirren could have drawn level shortly after the goal. A misjudgement from Ryan Porteous found Jon Obika in a dangerous position but the striker hesitated when a first-time shot might have beaten Chris Maxwell in goal.
Maxwell, though, was soon in danger early in the second half. He came out his box and tripped Magennis as the midfielder raced on to a pass forward. The home fans wanted a red card but the referee decided a yellow would suffice.
St Mirren continue to push but were not doing enough to work the goalkeeper. Mullen came on and sent another shot high over the bar, before sending in a bending shot that struck the post.
Hibs claimed a second goal from the penalty spot after 82 minutes. Gary MacKenzie fouled substitute Martin Boyle and Mallan converted the kick.
Morias gave St Mirren a late lifeline when he converted after Mullen's shot had been saved but there was not enough time for the home side to claim an equaliser.