The Celts took the lead in the 14th minute through Reo Hatate amid a vicious period of dominance.
It would become 2-0 just four minutes later, when Kyogo Furuhashi smartly found the back of the net.
The Japan star made it a brace a few minutes before half-time to put Celtic in cruise control.
Shortly after the break, Hatate got a brace of his own to put the match well beyond any doubt at 4-0
St. Johnstone, despite being dominated for much of the 90 minutes, made good on one of their three shots on target, as Drey Wright beat Joe Hart to make it 4-1.
David Turnbull picked up a booking in the 92nd minute and was shown a red in the 96th.
Celtic's win means they've reinstated their nine-point lead over Rangers at the top of the Premiership.
St. Johnstone missed out on a chance to move above Hearts and are now likely to surrender fifth to St. Mirren, who are on the same points but have two games in-hand.
