Neil Lennon’s side sealed a return to Hampden Park after first-half goals from the Irish striker and Joe Ledley proved sufficient to see off a determined Buddies outfit
Portuguese striker Esmael Goncalves had got the Paisley side back on level terms following the Welshman's goal, but the hosts were held off during a tight second half.
Danny Lennon opted to leave Graham Carey on the bench along with Sam Parkin and Lewis Guy, while David Barron missed out completely, with David van Zanten, Gary Teale, Stephen Thompson and Goncalves all starting.
The visitors made four changes from the side that suffered defeat away to Motherwell on Wednesday, with Tom Rogic, Beram Kayal, Kris Commons and Georgios Samaras being replaced by Kelvin Wilson, Efe Ambrose, Gary Hooper and Ledley.
With five minutes gone the SPL leaders took the lead as James Forrest raced down the right wing before crossing into the box for Ledley to head home from close range.
However, the visitors then handed St Mirren an equaliser as John McGinn played a long ball into the box which Emilio Izaguirre somehow managed to head beyond his own keeper Fraser Forster, allowing Goncalves to knock the ball home from less than a yard out.
Neil Lennon’s side regained the lead midway through the first half after a well worked corner, which saw Forrest play a one-two with Hooper before crossing to the back post, where Stokes was left unmarked and slammed his header into the net.
Celtic continued to dominate the reminder of the first half, but couldn’t find a way past the Buddies defence in order to add to their advantage.
Both sides started the second half brightly, with Stokes having an effort for Celtic and Goncalves also trying his luck for the home side, but neither of them could find the necessary finish.
Just after the hour mark the visitors almost gifted St Mirren another goal, as Van Zanten raced down the right before crossing to the near post where Forster and Thomas Rogne almost got in each other’s way.
The Parkhead outfit should have sealed their place in the semi-final with just over 20 minutes left as Hooper pounced on a mistake by Lee Mair and smashed the ball towards goal but, unfortunately for the striker, Samson got a hand to the ball to push it onto the bar.
St Mirren should then have claimed a replay in Glasgow as substitute Carey smashed a free kick round the wall from the edge of the area which Forster somehow managed to punch away from danger.
The Paisley side continued to push in search of the equaliser, but they couldn’t find the killer ball to open up the Celtic defence and Neil Lennon’s side comfortably took their place in Monday afternoon’s semi-final draw.