The Hoops’ 7-1 League Cup final win over the Light Blues at Hampden Park in 1957 is the club’s biggest victory in the derby match and the gap between the two sides was every bit as big at Celtic Park.
Odsonne Edouard, the 20-year-old French striker on loan from Paris St Germain, scored a first-half double with James Forrest adding a third before the break with midfielders Tom Rogic and Callum McGregor notching further goals early in the second-half.
Goalkeeper Jak Alnwick, making his Old Firm debut, made several good saves to keep the champions at bay and leave ragged Rangers relieved they had not encountered further damage.
Rodgers, whose side beat the Govan men 4-0 in the William Hill Scottish Cup semi-final two weeks ago, said: “We should have had seven but we will take five.
“We scored five but it was probably going on seven or eight.
“Their keeper made some great saves.
“It was great tribute to the work of the players and the scrutiny that they are under. The performance was outstanding, if you think of what the players put into the game.”
Rodgers insists the league title win was better than last year when they went unbeaten in 38 games.
Celtic have lost to Hearts, Kilmarnock and Hibernian this season but the former Swansea City and Liverpool boss added: “This title is definitely better that last year - even though we went unbeaten last year.
“OK, there was expectation of course but to then to have had that season and to come into this season with virtually very little to break, and to go and perform like we have done for quite a number of games under pressure, we have done really well.
“I am really proud of the players. I don’t think I could have asked for any more.
“There won’t be too many atmospheres around the world like today.
“It was great to make supporters happy, it was a special day for them.”
Neither Rangers boss Graeme Murty or any of his team went into the media room for comment after the match.