The Hoops opened the scoring in the 14th minute through Odsonne Edouard before the French striker completed his brace and began the humiliation in the shadows of half time, with winger James Forrest striking on the 45 to make it a three-goal lead at the break.
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.
After chairman Dave King cast fresh doubt on whether the ex-Scotland global defender would have his contract renewed in the summer - ahead of the Gers' 4-0 Scottish Cup semi-final hammering from Rodgers' rampant Celts in the William Hill Scottish Cup semi-finals - it emerged that Steven Gerrard was the frontrunner to take over in the build-up to yesterday's confrontation.
"You have to think there's some credibility in what they're trying to do".
Celtic are now unbeaten in the last 11 games against Rangers - winning nine and drawing two.
Rangers are in danger of finishing fourth in the Scottish Premiership this season.
However, it would appear that Police Scotland weren't quite so impressed.
"I am really proud of the players".
Skipper Scott Brown insisted it was an honour to be part of the side that won the club's seventh successive title at Parkhead.
"This will live with us for the rest of our lives", Celtic captain Scott Brown said.
"The sun was shining and it was against Rangers as well, it was all about our performance today". "To do it in the style we did is just fantastic".
Murphy said: 'The only thing with that, I was thinking really, is that how do you get concrete reassurances with something like that?
"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".
On Gerrard, Rodgers added: "From Stevie's perspective, I know he has always wanted to manage". I love the role and will do everything I possibly can to keep it.