Hoops captain Callum McGregor underlined the difference in class between the bitter Glasgow rivals with a brilliant strike to round off the victory at Parkhead.
McGregor's rocket came after first-half goals from Daizen Maeda and Kyogo Furuhashi as Celtic went to the top of the table, above Aberdeen on goal difference, thanks to their fourth successive win.
Celtic are already five points ahead of Rangers, who were beaten for the first time in the league this season.
Celtic adapted seamlessly to the departure of Matt O'Riley to Brighton earlier in the week as Paulo Bernardo produced a first-half display bursting with energy and invention.
New signings Arne Engels and Luke McCowan came off the bench to offer a glimpse of their potential as Celtic fans lapped up their team's dominant display.
Rangers' bright start proved a false dawn as Cyriel Dessers shot straight at Kasper Schmeichel before being flagged offside and Rabbi Matondo headed wide from six yards.
Celtic showed how clinical they could be when they beat the press with the help of a flick by Reo Hatate.
McGregor sent Nicolas Kuhn away and the winger squared for Furuhashi to finish, however the goal was disallowed by VAR for offside against the German.
Rodgers' men went ahead in the 17th minute when Bernardo found Alistair Johnston's run and the full-back's pass was swept home by Japan star Maeda.
The Hoops doubled their lead five minutes before the break as Greg Taylor fed Furuhashi, who punished keeper Jack Butland's questionable positioning by slotting into the net from 25 yards.
Ross McCausland dispossessed Bernardo and set up Dessers immediately after the interval, but Schmeichel dived to save before John Souttar had an effort blocked.
Celtic were still capable of cutting Rangers open and Hatate played Furuhashi in but the striker's chip drifted just wide.
Rodgers handed a first appearance to record signing Engels in the 62nd minute.
And McGregor capped Celtic's day to remember in the 75th minute, bursting forward, producing a body swerve to open up the shooting chance and curling his long-range strike into the top corner.
