A 15-minute first half goal blitz earned Celtic all three points at McDiarmid Park.
But a late comeback almost salvaged an improbable point for a St Johnstone team that refuse to give up.
Leigh Griffiths, Scott Sinclair and James Forrest did the damage in an opening period that St Johnstone were second best in by a distance.
The second half was an improvement though, and there was a late penalty goal from Danny Swanson, and an even later Steven MacLean strike.
But, with the game surprisingly back in the balance in injury time, Ryan Christie finished it off with Celtic’s fourth.
It didn’t take much time for the game to settle into a pretty one-sided rhythm, with the visitors dominating the ball.
For all the Celtic possession though, it wasn’t actually until 15 minutes that they threatened through a Sinclair free-kick that flew across the face of Alan Mannus’s goal.
There was a Tom Rogic run into the box from midfield that was snuffed out by Mannus but a makeshift defence – which was without injured Steven Anderson and had new signing Richard Foster at right-back – was coping quite well in the early stages.
Saints weren’t offering much going forward and, in a rare counter-attack on 22 minutes, Murray Davidson didn’t take advantage of a good shooting opportunity 20 yards from goal.
The Perth defensive resistance was broken on 28 minutes when Kieran Tierney sent over a cross from the left and Griffiths’ deflected shot gave Mannus no chance.
Saints nearly hit back on the half-hour when a David Wotherspoon free-kick was tipped over the bar and from the corner that followed, the ball broke to MacLean six yards out. However he couldn’t get a strong enough connection on his first time shot.
That was as good as it got for Tommy Wright’s men in the first half, with two more goals conceded in the last five minutes.
You had to feel sorry for Mannus, who made a fine double save to deny first Forrest and then Griffiths, but a triple save was beyond the Northern Irishman and Sinclair found the back of the net.
Then with two minutes left before the break Forrest had the Saints defence back-pedalling after Brad McKay lost out to Griffiths on the half-way line, and he finished off the run all by himself with a lovely finish.
Celtic kept up the pressure after the re-start and Rogic struck the bar with a long-range shot.
Brendan Rodgers must have felt the three points were in the bag as star man Griffiths was brought off on 55 minutes, no doubt with Celtic’s Champions League trip in mind, replaced by Moussa Dembele.
For Saints, Liam Craig had replaced Blair Alston a couple of minutes earlier.
Much of the second half was a bit of a non-event but there was a late consolation for Saints when Swanson was tripped in the box and he scored from the penalty.
Then in the 89th minute Swanson drilled the ball across the six yard line and MacLean bundled the ball just about over the line.
Mission Impossible wasn’t completed however as Celtic scored again in injury time through Christie.
