Celtic were more comfortable winners in Paisley than the scoreline suggests as first half goals from Callum McGregor and James Forrest put them in command.
St Mirren goalkeeper Vaclav Hladky made a string of second half saves from Forrest, Jeremie Frimpong, Odsonne Edouard and Olivier Ntcham to prevent the visitors bolstering their goal difference.
And the Buddies even made Neil Lennon's men sweat in stoppage time after Cameron MacPherson's free-kick pulled a goal back a minute from time.
"We were a bit slow getting our shots off at times but I thought we looked dangerous all day," said Lennon. "I would like us to put a more flattering scoreline on the board, but in terms of the performance, it was good."