Second-half goals from James Forrest and Stefan Johansen took the visitors a step closer to the treble and left St Mirren four points adrift at the bottom.
Ronny Deila’s side, up against opponents other than Dundee United for the first time in a month, were kept honest without ever looking in trouble on a night when Craig Gordon did not have a difficult save to make.
Stephen Mallan and Yoann Arquin did find the target before half-time, but Gordon was well-place to deal with both and it was the goalkeeper’s opposite number Mark Ridgers who caught the eye.
Twice he denied Celtic a half-time lead with real agility, getting down low to keep out Kris Commons and Forrest, and when he was beaten after the break Stuart Armstrong’s deflected shot just missed a post.
Mallan’s long-range effort briefly had Gordon worried before drifting off-target, but that was as good as it got for the home side as Forrest finished off Adam Matthews’ good work for the opening goal (64).
Johansen added a second from the penalty spot (80) after a Viktor Genev handball, and substitute Gary Mackay-Steven was close to a third late on.