Virgil van Dijk opened the scoring on 26 minutes and Leigh Griffiths doubled the home side's advantage before the interval.
Substitute Mikael Lustig then scored a late brace with a left-foot shot and a header to send Celtic a point clear of Aberdeen, having still played a game less.
Meanwhile, Kris Doolan was the toast of Partick Thistle after netting four times in their 5-0 demolition of Hamilton at Firhill.
The striker produced a clinical display of close-range finishing to strike with both feet and his head before Nathan Eccleston completed the rout in the closing stages.
Fourth-placed Dundee United had to come from behind to secure a share of the spoils in a 1-1 draw at St Mirren, with Stuart Armstrong levelling after Kenny McLean had broken the deadlock with a superb finish.
A Greg Stewart penalty proved enough to give Dundee a 1-0 victory against Kilmarnock at Dens Park after Lee Ashcroft had brought down Jim McAlister after 19 minutes.
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