The French forward beat the offside trap and guided a cool finish under Allan McGregor in the 32nd minute to set up a clinical victory at Ibrox for his side.
Substitute Jonny Hayes added a second on the counter-attack in stoppage-time before Jordan Jones compounded the home side's misery by wiping out Moritz Bauer and earning himself a straight red card.
Neil Lennon's Celtic needed a boost after being dumped out of UEFA Champions League qualifying at the hands of CFR Cluj in August — a blow softened only slightly by successfully reaching the UEFA Europa League group stage.
The surgical manner of this triumph should inspire even greater confidence that a ninth successive league title is its to lose.
Hatem Abd Elhamed recovered from injury to replace Kristoffer Ajer on the right side of Celtic's defence and he was at the centre of an eventful first 15 minutes.
The Israel international made a crucial last-ditch challenge to prevent Rangers striker Jermain Defoe from pulling the trigger in the early stages and then required treatment after an aerial collision with Jon Flanagan.
Chances became scarce until James Tavernier gifted possession to Michael Johnston, who drove forward and threaded Edouard through on goal for the opener.
Rangers boss Steven Gerrard turned to Alfredo Morelos on the hour, removing the largely ineffective Defoe.
Another substitute, Sheyi Ojo, had finally tested Fraser Forster moments earlier, but there was precious little else for the on-loan Hoops goalkeeper to do.
McGregor kept Rangers in the contest with a trio of good stops but, after denying Hayes once, he could not keep the winger from bundling in the rebound, three minutes before Jones's rash challenge, which left Gerrard shaking his head in frustration on the sidelines.