Returning Hoops' striker Leigh Griffiths opened the scoring from a Nir Bitton pass after 35 seconds, beating the debut goal from Gary Mackay-Steven against Partick Thistle on Wednesday night by three seconds.
When midfielder Stefan Johansen doubled the visitors' lead seven minutes after the break it looked like Ronny Deila's side would go on to strengthen their grip on the game.
Perth midfielder Michael O'Halloran, however, reduced the deficit in the 72nd minute to end Craig Gordon's eight-game clean sheet run, although the Parkhead keeper denied the home side twice in the frantic finale.
Celtic go six points clear of Aberdeen - the Dons have the chance to reduce the deficit at Hamilton on Sunday albeit they will have played a game more - and will go into the first leg of their Europa League last-32 tie against Inter Milan at Parkhead with growing confidence.
With such an important European game coming up, there was some surprise that Deila made only one change.
Griffiths returned from an ankle knock to replace John Guidetti, who dropped to the bench and that alteration was vindicated within seconds of the start when the former Wolves player put the visitors ahead.
Bitton split the Saints defence with a through ball allowing Griffiths to race through between Tam Scobbie and Steven Anderson and slip the ball past St Johnstone keeper Alan Mannus for his fourth goal in five games.
The home side, who showed four changes with midfielders Lee Croft, Chris Millar and O'Halloran and striker Steven MacLean coming in, were stunned but to their credit composed themselves.
In the 12th minute, Hoops keeper Gordon saved a close-range toe-poke from O'Halloran, before the Perth side were dealt another blow, midfielder Murray Davidson hobbling off to be replaced by Chris Kane.
Griffiths almost grabbed a second when defender Virgil van Dijk headed down a Stefan Johansen corner but this time the Parkhead forward could not get a proper connection and Mannus gathered.
Moments later, Kane glanced an O'Halloran cross from the left inches past the far post with Gordon beaten.
Play flowed from end to end
Mannus made two saves from Griffiths in quick succession before Kane should have done better with a free header from a Simon Lappin corner, the striker clearing the crossbar.
In the 33rd minute a brilliant save on the stretch from Mannus denied Mackay-Steven at the expense of a corner, which came to nothing and the first-half ended pretty even.
Celtic, though, struck early in the second-half which looked to put the Parkhead side in a commanding position.
Stuart Armstrong's chip into the box in the 52nd minute was headed down by Griffiths to Johansen who took the ball on his chest and despite the attention of Scobbie and Anderson, rifled it low past Mannus from six yards.
With one eye on the visit of Inter, Deila replaced Griffiths with Anthony Stokes and Armstrong with Liam Henderson.
In between, St Johnstone midfielder Croft, belatedly booked for taking out Johansen off the ball, was replaced by James McFadden
Saints' goal, which made the latter stages interesting, came out of the blue.
Kane stretched but failed to get on the end of Scobbie's low deflected cross from the left but the ball hit Gordon's knees and fell to O'Halloran who knocked it high into the net from six yards.
Deila brought on Efe Ambrose for Mackay-Steven with eight minutes remaining to give Celtic more defensive solidity.
In the 86th minute Saints' left-back Brian Easton blocked a net-bound shot from Henderson, who had been set up by Stokes.
But Gordon made a great double save near the end, first from substitute Brian Graham's header and then skipper Dave Mackay's volley, to ensure the points went back to Glasgow.
Source : PA
Source: PA