Midfielder Callum McGregor, who only started because Stuart Armstrong pulled up with a tight hamstring in the warm-up, gave the home side the interval lead with a well-taken drive.
Winger Scott Sinclair, who started the game as centre-forward as Moussa Dembele and Leigh Griffiths missed out with respective knee and calf injuries, grabbed a double - the second from the spot in the dying stages - with the impressive Patrick Roberts also notching.
The victory extended Celtic’s unbeaten domestic run since the start of the season to 27 games, one more than Jock Stein’s all-conquering side of 1966-67.
Current Hoops boss Rodgers said: “It is a huge honour of course. The history of this club, 129 years, and obviously how difficult that is.
“It is an incredible run and every accolade they get they deserve because of their focus, the spirit within the team and the quality of the football they are producing.
“We are very proud but we have set the challenge going forward.
“We have to keep winning and that comes from our work, our concentration and making sure we take care of all the background noise that goes around them and just focus on the job. The players were magnificent.”
The Hoops’ 17th consecutive Premiership victory restored their 22-point lead at the top of the table over Old Firm rivals Rangers.
Midfielder Tom Rogic was also out injured, which served only to confirm further the Parkhead club’s strength in depth as they motor towards their sixth-successive title.
Rodgers said: “It shows how well the players work together, the different ideas which they can take on board.
“We tried to play Scott through the middle, then we switched him into his natural position and Patrick came in and played as a central striker and I thought he was outstanding in that role.
“It was an outstanding team performance but above all of that, our ability to press the game was outstanding.”
Hearts head coach Ian Cathro admitted his concern over defender John Souttar, who was carried off on a stretcher late in the match with an Achilles injury.
He said: “There was a challenge and then he landed awkwardly. There is a bit of concern just now, it is an Achilles issue.
“We don’t know the extent of it but, as you saw, it didn’t look nice.
“It will be in the next few hours and tomorrow morning before we know exactly what it is.”
Cathro might have to move for a centre-back before the January transfer window closes.
However, he confirmed interest in former St Mirren loan striker Esmael Goncalves, the 25-year-old on the books of Cypriot outfit Anorthosis Famagusta, and 31-year-old Greek international midfielder Alexandros Tziolis, who is a free agent after leaving PAOK Salonika.
Cathro said: “It has already been spoken about probably from the other end in the case of Goncalves, and Tziolis is now a free agent.
“We are working on both of those things. It is possible but there is still a little bit of work to be done.”