Mark O’Hara converted an early penalty for the hosts after VAR ruled Greg Taylor had handled, but the hosts had Charles Dunne sent off for pulling back Kyogo Furuhashi when he was in on goal.
Jota levelled and Alistair Johnston forced the ball in off O’Hara for Celtic’s second, with Liel Abada and Matt O’Riley’s strikes and Oh Hyeon-Gyu’s penalty completing the rout.
With a vastly superior goal difference to nearest challengers Rangers, Celtic effectively need eight more wins from their remaining 11 games to retain their title.
St Mirren remain sixth, having been overtaken by Aberdeen on Saturday.