First-half efforts from Jeffrey Schlupp - his first for the club, cleverly finding the inside of the post from the left of the area - and an Arne Engels penalty had Celtic ahead at the interval.
However, the goal of the half came in between, courtesy of a brilliant, curling free-kick from the left boot of St Mirren wing-back Declan John.
There were also a couple of superb Kasper Schmeichel saves before that, denying first Toyosi Olusanya, when the striker was played in behind the Celtic defence, then Mark O'Hara after the Buddies captain shot on the turn from inside the area.
After the break, right-back Ryan Alebiousu made up for the sloppy concession of Celtic's penalty by playing a key role in the Buddies' second equaliser, slammed into the turf and over the despairing Schmeichel by Killian Phillips.
Celtic's superior squad depth proved too much for St Mirren, however, with Yang, Jota and Luke McCowan all coming on to make important contributions, with McCowan cracking a fine shot off a post with 10 minutes to go in addition to the champions' late goal blitz.