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. Midfielders Tom Rogic and Callum McGregor notched 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 Scottish Cup semi-final two weeks ago, said: “We should have had seven, but we will take five.
“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.”
Rodgers’ side have now moved to within a Scottish Cup final win over Motherwell of an historic second successive domestic treble.
Skipper Scott Brown insisted it was an honour to be part of the Celtic side to claim the latest title success in such style.
Midfielder Brown, 32, who has now won eight titles since joining Celtic from Hibernian in 2007, said: “It was lovely, the way we’ve done it.
“The sun was shining and it was against Rangers, as well. It was all about our performance today.
“We let ourselves down last week against Hibs, but we managed to bounce back, and we bounced back in style.
“We worked on how we were going to press all week and we demonstrated that out on the park.
“The title hasn’t been won against Rangers for a long time and it is great. It is a great honour to be here when we’ve done it.
“To do seven in a row as well is fantastic, but there is a lot more work ahead now, a few more games before the Scottish Cup final.”
Asked if it was his best game in football, Edouard, speaking through an interpreter, said: “Certainly, I am going to remember this all my life, because it is my first title.
“I am very happy for the team and myself, and to be able to win the title against Rangers in front of our fans is a pleasure for everyone.”
When asked if the title win would make him want to make his move to Parkhead permanent, Edouard added: “Most important thing is we have won the title today, the season is not over.
“We have the Scottish Cup final to play and, hopefully, after that there will be time for discussing options.
“I love this club and, if the decision was up to me, I would like to stay, but I can only do so much.”
Neither Rangers boss Graeme Murty nor any of his team went into the media room for comment after the match.
Gordon, Lustig (Hendry 71), Boyata, Ajer, Tierney, Ntcham, Brown, Forrest, Rogic (Sinclair 67), McGregor, Edouard (Griffiths 75)
Simunovic, Roberts, Bain, Eboue.
Alnwick, Tavernier, McCrorie, Martin, Halliday, Holt, Dorrans (Docherty 71), Candeias, Windass (Morelos 57), Murphy, Cummings.
Goss, Hodson, Rossiter, O’Halloran, Kelly.