Midfielder Kris Commons, who shrugged off a nasty ankle injury to make the game, drove the home side into the lead in the 14th minute and then grabbed a poacher's second the 51st minute before defender Mikael Lustig grabbed the third just after the hour mark.
With closest challengers Motherwell drawing 2-2 at home with St Mirren it means Celtic, with five games remaining after the split, go 15 points clear with a massive goal advantage and while there is no doubt about the destination of the title, Hoops fans will have to wait a bit longer before it is official.
James McFadden added to his collection of spectacular goals to rescue a deserved point for Motherwell and edge them closer to a European spot after a 2-2 draw with St Mirren.
The Scotland international curled home a free-kick with five minutes left after Saints had come from behind to take the lead in this Clydesdale Bank Premier League match.
Conor Newton's long-range strike had cancelled out Michael Higdon's 23rd goal of the season and Lewis Guy struck in the 75th minute after Motherwell had come close on numerous occasions in the second half.
But McFadden the final say to ensure Motherwell finished the weekend as they started it - three points clear of Inverness in second place and eight points ahead of the chasing pack in the race for a Europa League slot.
Kilmarnock saw their hopes of a place in the top six blown apart as Dundee came up with a 2-1 victory that spares them relegation from the top flight for at least another week.
Former Rugby Park playmaker Gary Harkins returned to Ayrshire for the first time since his move to Dens Park but made himself most unwelcome with a goal in either half.
Kris Boyd had levelled just four minutes before Harkins' decisive second to extend his record-breaking tally of SPL goals to 166, but just as they looked set to sneak through on goal difference, Rory Boulding's last-gasp winner for Dundee United against Aberdeen saw the Tannadice men snatch Killie's place in the top half of the table.
Killie had been in the driving seat to claim the top six berth, with United, the Dons and Hibernian also in contention at the start of the day.
The eventual outcome meant a disappointing end to Aberdeen boss Craig Brown's 36-year managerial career as he now steps aside for Derek McInnes to take over the reins at Pittodrie.
- Sports & Recreation
- Mikael Lustig
- St Mirren