A double from Virgil van Dijk (41 and 53 minutes) put Celtic in charge, and although Ross pulled a goal back through Ivan Sproule, the visitors wrapped up the win with a quickfire brace from Joe Ledley (70 and 73).
Aberdeen slip to third behind Inverness following their loss to rock-bottom Hearts, although the Dons only had themselves to blame for throwing away a match in which Niall McGinn had given them the lead.
McGinn subsequently missed a penalty before midfielder Barry Robson was sent off in the 55th minute.
Hearts then made the most of their man advantage by netting three times in the final 24 minutes to take the points, Jamie Walker, Callum Paterson and Ryan Stevenson the men on the scoresheet.
Inverness moved two points above the defeated Dons with a 2-0 win at Hibernian.
First-half goals from Nick Ross and Billy McKay secured three points for Inverness, whose manager Terry Butcher is being tipped to be named as Pat Fenlon's successor at Easter Road on Monday. Butcher watched on from the main stand at Saturday's game.
Fourth-placed Motherwell also slumped to defeat as they were beaten 4-0 at home by Dundee United, crushing hopes of a sixth successive home win for Stuart McCall's men..
Two goals from Ryan Gauld and one each for Paul Paton and Andy Robertson saw the visitors to victory.
Partick Thistle remain without a win at home in the Premiership this season after two goals by Steven Thompson guided St Mirren to a 3-0 victory at Firhill.
The double by Thompson and one from Conor Newton were enough for Danny Lennon's men to take the three points back to Paisley.
In Saturday's other game, St Johnstone defeated nine-man Kilmarnock 3-1.
Nigel Hasselbaink opened the scoring before Stevie May netted a brace, one from the spot, to make it 3-0.
Sean Clohessy's freak cross was little more than a consolation goal for the Ayrshire outfit who had Jackson Irvine and Darren Barr red-carded in the second half.