The Hoops retained their five-point lead over Old Firm rivals Rangers by dominating the Jambos, who had won 10 of their past 11, culminating in the weekend's victory over 'Gers at home.
Celtic's goals came through teenager James Forrest in the 5th minute before Anthony Stokes helped himself to a second-half double and then Paddy McCourt supplied the finishing touch with ten minutes remaining.
Celtic boss Neil Lennon was delighted with the performance at Parkhead and feels Hearts were simply in the wrong place at the wrong time.
"It's been coming. The level of play in recent weeks has been good, we just haven't been putting teams away," Lennon said.
"It came together tonight and it was as good a performance as we've had at home all season against a very confident team.
"I thought we were absolutely brilliant from start to finish.
"There were some great individual performances but as a collective they were excellent.
"There was a real intensity to their play and the pleasing thing was we picked up where we left off in the first half and never gave Hearts a minute.
"There was a real hunger. It was a big game for us and they did everything we asked of them and it could have been even more.
"We looked a good team out there tonight and the players have set themselves a benchmark.
"The only downside was Forrest, it looked like it could have been a hamstring injury but he will have a scan in the morning."