Hit by a raft of COVID-19 cases, with manager Steven Gerrard among those isolating, Scottish champion Rangers still had the better of this latest chapter in the derby and found a deserved breakthrough in the 66th minute thanks to Filip Helander's brilliant goal.
Helander met Borna Barisic's corner with a thumping header to score his first Old Firm derby goal, sending a vociferous, albeit wholly one-sided because of coronavirus restrictions, Ibrox crowd into ecstasy.
Ryan Kent had previously hit the post for Rangers, with Helander's header punishing the profligacy of Celtic forward Odsonne Edouard, who missed a golden chance midway through the first half as the Hoops' winless run against their Glasgow rivals in the league was extended.
An enthralling, end-to-end start should have culminated in Celtic taking the lead in the 25th minute, yet Edouard – hunting his eighth league goal against Rangers – somehow skewed wide of a gaping goal from five yards out.
Kent did much better at the other end seven minutes later, beating Joe Hart with a sublime curling effort, but the upright came to Celtic's rescue.
Playmaker Kent tried another curler on the stroke of the hour, only to send his strike straight at Hart for a comfortable save.
Rangers' pressure finally told after the hour, however – Helander rising to meet Barisic's inswinging delivery, with Hart unable to keep out the centre-back's towering header.
Helander almost went from hero to pantomime villain straight from the restart when his slip enabled Kyogo Furuhashi to steal in, but on his league debut for Rangers, stand-in goalkeeper Robby McCrorie made a fantastic save to spare his team-mate's blushes and seal victory.
Rangers cruised to the title as Celtic capitulated last season, but the Hoops look a different proposition under Postecoglou, though he has now become the first manager to lose his first league Old Firm derby match in charge of Celtic since Tony Mowbray in October 2009.
Gerrard would have been kicking every ball from home during the contest, no doubt, and given the adversity Rangers faced this week, not to mention a gruelling trip back from Armenia, it feels like a statement win from the champion.
Celtic hosts Ross County after the international break, while Rangers faces St Johnstone, both matches scheduled for 12 September (AEST).