Liel Abada scored a first-half double, one either side of a glorious Jota chip, to have the points secured by the interval.
Substitute David Turnbull accepted a gift from Jon McLaughlin to slam the ball past the Gers goalkeeper for number four to take Celtic five points clear of the Ibrox side at the top of the table, after just six fixtures.
The Hoops boss reiterated that the lead means little at this stage of the season but likes the way his side are playing - they have scored 17 goals in the last three games - and was encouraged by an "outstanding" performance.
Postecoglou said: "The league table isn't important right now. What's important is how we play.
"If we continue to play like that, absolutely, we're going to be hard to stop. That's our intent. We want to be better.
"We've started the season really strongly but we've got stronger each week and today was another strong performance.
"People have been dismissive because they thought the opposition we've had so far weren't up to it.
"We were brilliant last week but people spoke about how poor Dundee United were (Celtic won 9-0 away from home).
"That suits us because it ignores our part in it. It will be the same today.
"We'll just keep doing what we're doing. Five points doesn't get you anything right now - that was shown last year.
"But if we keep improving and playing like that? We'll be hard to stop."