Martin O'Neill's men seemed to be suffering a hangover from Wednesday night's defeat to Bayern Munich and could not find a way through Terry Butcher's men in the first half.
However, Swedish hit-man Henrik Larsson - 32 on Saturday - headed The Bhoys ahead from an Alan Thompson free kick just two minutes after the break.
Further strikes midway through the second period from Chris Sutton and Shaun Maloney - a superb free kick - gave the scoreline a more comfortable feel, though the visitors battled gamely.
Dundee maintained fourth spot after seeing off a disappointing Aberdeen outfit at Dens Park.
Veteran full back Tom Cowan opened the scoring for The Dark Blues after 28 minutes and Nacho Novo sealed victory with a second eight minutes before the end.
Dunfermline, playing the first game on their new artificial pitch, could only manage a goalless draw against mid-table rivals Hibernian.
Kilmarnock recorded only their second win of the new campaign with a 2-1 success at Livingston, despite finishing the game with only ten men.
Sean Hessey put Killie ahead on the quarter hour mark, though the lead was short-lived as Lee Makel levelled for the hosts just three minutes later.
Kris Boyd then scored the third goal in seven minutes to restore the visitors' advantage, and although Barry McLaughlin saw red on the hour mark, Killie held on for all three points.
Dundee United emerged triumphant in the battle of the bottom two, with a goal in either half from Charlie Miller enough to condemn Partick Thistle to defeat.
The former Rangers midfielder struck on 41 and 63 minutes to hand United their first victory of the new campaign, and move them above their opponents.
Click below for a match summary:
Celtic v Motherwell
Dundee v Aberdeen
Dunfermline v Hibernian
Livingston v Kilmarnock
Partick v Dundee Utd
Click here for the updated SPL table
