Anthony Stokes opened the scoring in the 55th minute when he rounded home goalkeeper Alan Mannus to score from a tight angle, while Nir Biton coolly converted from the penalty spot in the 75th minute after home skipper Dave Mackay earned a red card from referee John Beaton for bringing down Dutchman Derk Boerrigter. It looked to be a soft award from the Fifa whistler.
The champions made it 3-0 when Calum McGregor shot through the legs of Mannus in the 83rd minute to give Ronny Deila three points in his first league match in charge of the Hoops.
Partick Thistle - the other Premiership side playing their first league game of the new season - beat Ross County 4-0 at Firhill Stadium.
Stuart Bannigan opened the scoring for Alan Archibald's side in the 40th minute, with Frempah netting an own goal four minutes after the interval. Gary Fraser made it three in the 73rd minute and Stephen O'Donnell completed a great night for the Jags with the fourth.
Hamilton racked up their first win of the season against St Mirren in Paisley with goals from Ali Crawford in the 19th minute and an own goal by Marc McAusland in the 51st minute.
Stuart McCall's Motherwell went down 1-0 at Dundee United, with substitute Mario Bilate on target for Jackie McNamara's side.
At Rugby Park, Aberdeen bounced back from their opening-day defeat by Dundee United to beat Kilmarnock 2-0 through Peter Pawlett and Ryan Jack strikes, while Inverness Caley drew 0-0 with Dundee.