Ange Postecoglou's side went into the contest with the league's only remaining 100% record, and they blew their Glasgow neighbours away inside the first half at Celtic Park as Rangers fell to their first defeat of the campaign.
A brace from Liel Abada either side of Jota's strike sent Celtic into the break with a commanding lead, and they added to that 10 minutes from time when David Turnbull capped off a famous triumph.
The deadlock was broken after only eight minutes when Abada continued his fine start to the season with the opening goal, latching on to a loose ball inside the box and putting just enough on his shot to beat the keeper.
Jota doubled the advantage with a dinked finish at the end of a quick team move shortly after the half-hour mark, before Abada doubled his personal tally five minutes before the interval.
Postecoglou's men did not need a helping hand to add further gloss to their victory, but they received one nonetheless as Rangers keeper Jon McLaughlin compounded the visitors' misery by giving the ball straight to Turnbull, who accepted the gift with glee to add a fourth 12 minutes from time.
The result means that Celtic have now made their best-ever start to a season, winning all six matches while scoring 25 goals and conceding just once.
The Bhoys will now look ahead to Tuesday's Champions League glamour tie at home to holders Real Madrid, whereas Rangers must regroup from only their third defeat in their last 42 league games before taking on Ajax in Amsterdam on Wednesday.