Not since 1898-1899 have the Gers gone a full top-flight season without defeat – then winning all 18 matches – but Celtic, itself 'invincible' in 2016-2017, failed to halt their latest bid.
Kemar Roofe chested in a smart opener after 26 minutes and Callum McGregor was sent off for a foul in the build-up to that goal, putting Steven Gerrard's side in control.
Although Celtic quickly responded with Odsonne Edouard's close-range header, Alfredo Morelos blasted Rangers back into the lead before Roofe and substitute Jermain Defoe added to the advantage in the second half.
A sublime Allan McGregor stop from Mohamed Elyounoussi, who netted in the sides' previous meeting, set in motion a frantic game-turning stretch after a quiet start.
Callum McGregor had been booked just prior to that Elyounoussi effort and then foolishly lunged in on Glen Kamara, although referee Nick Walsh allowed play to continue and Roofe redirected Ryan Kent's wayward shot in before a second yellow card was shown.
Allan McGregor was soon in action again to touch Jonjoe Kenny's cross away, though, and Kristoffer Ajer was up highest from the subsequent corner to nod across goal for Edouard to beat Steven Davis on the line.
But back Rangers came and Scott Bain saved from both Roofe and Joe Aribo yet could not deny Morelos, who broke his Old Firm duck in March and deceived Scott Brown to shoot into the roof of the net.
David Turnbull mistimed a header early in the second half, but Roofe made no mistake from Borna Barisic's measured centre to put the result beyond doubt.
There would be no Roofe hat-trick as he made way for Defoe, yet the substitute got among the goals with a cool finish in the 92nd minute.
Even if Gerrard's men slip up in the final weeks of the season, they will end the campaign without having lost to Celtic in the league for the first time since 1999-2000.
Celtic, which also lost to Rangers in the Scottish Cup, had four flawless Old Firm seasons in the intervening period (2001-2002, 2003-2004, 2016-2017, 2017-2018).
Rangers must negotiate matches with Livingston, on 13 May (AEST), and Aberdeen on 15 May in order to finish the season undefeated. Celtic plays next against St Johnstone on the same night as the champion's trip to Tony Macaroni Arena.