Winger Patrick Roberts struck twice in the first 20 minutes and Mikael Lustig added the third for Celtic four minutes after halftime.
Niall McGinn and Andrew Considine pulled two goals back for the visitors but Celtic hung on to move 12 points ahead of Aberdeen in the table with two games left.
"It means we are the best team in Scotland," Celtic manager Ronny Deila said.
"In the league we have been consistent but the last two months we have not had the same drive and energy in the team," added the Norwegian who is leaving Celtic at the end of the season after two years in charge.
"There have been some bad results which make the season a bit grey, rather than white," Deila said.
It was the 47th Scottish league title in Celtic's history, seven behind their arch-rivals Rangers who will return to the top flight next season after four years in the lower divisions following the club's liquidation in 2012.
(Reporting by Ed Osmond, editing by Alan Baldwin)
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