Second-half goals from Anthony Stokes, Callum McGregor and Nir Biton's penalty got the champions off to a winning start, as new manager Ronny Deila made a successful league bow.
The Glasgow club won the title at a canter last season, finishing 29 points ahead of second-placed Motherwell to clinch their third straight crown.
However, it has still been a close-season of change at Celtic Park after manager Neil Lennon resigned from his post, prompting Deila's arrival in June.
They also faced the unfamiliar position of playing catch-up on the rest of the division, with their opening-weekend clash against Partick Thistle postponed with Celtic Park still being reconverted for football use after hosting the Commonwealth Games.
But after taking some time to get going on Wednesday, Celtic soon returned to business as usual.
Stokes fired them ahead in the 55th minute when Kris Commons' sliding tackle played him in and the Irishman slotted home, before Derk Boerrigter was upended in the box 21 minutes later.
Saints defender Dave MacKay was shown a second yellow card for that challenge, giving Biton the chance to score from the spot.
A swift break down the right then ended with youngster McGregor adding the third with six minutes left, as Celtic comfortably claimed the points.
Partick Thistle also got their campaign off and running, as two goals in 15 minutes either side of the break set them on the way to a 4-0 win over Ross County.
Stuart Bannigan broke the deadlock five minutes before the interval, with defender Benedict Frempah then turning the ball into his own net 10 minutes after the restart.
County never looked likely to find a way back from there, and late goals from Gary Fraser and Stephen O'Donnell merely confirmed the rout.
Early pacesetters Dundee United kept their grip on top spot as they beat last year's runners-up Motherwell 1-0 courtesy of Mario Bilate's strike seven minutes from time.
Meanwhile, United's city rivals Dundee shared a 0-0 draw with Inverness Caledonian Thistle.
Ryan Jack's 71st-minute strike set the seal on a 2-0 win for Aberdeen at Kilmarnock after Peter Pawlett had latched on to Jonathan Hayes' pass to break the deadlock on the stroke of half-time.
And Hamilton Academical bounced back from an opening-weekend defeat to Inverness to put their first points on the board, with Ali Crawford and Marc McAusland's own goal seeing them past St Mirren 2-0.