It was a dream return to Celtic Park for Arzani and a measure of sweet revenge as the Australian struggled for game time during an unsuccessful two-year loan stint at the Glasgow giants.
It will also serve as a timely reminder for Socceroos manager Tony Popovic, who left the striker out of his squad for the recent World Cup, with the national team in action against Brazil later this month.
Arzani picked up the ball on the edge of the box before unleashing with his right into the top left-hand corner giving Celtic keeper Viljami Sinisalo no chance.
Commentators described the goal as a "stunner" and a "sensational strike."
In other action, Bournemouth enjoyed a dream debut in European competition with a 2-1 win at Real Sociedad in their Europa League opener.
The Cherries' German coach Marco Rose is no stranger to Europe given his previous experiences with the likes of Borussia Dortmund, but even he would have been surprised with how his Premier League team dealt with the European regulars in San Sebastián.
Justin Kluivert guided home the first and Rayan's clever header had them 2-0 up inside 20 minutes.
Sergio Gómez's cross drifted straight in on the hour, but the visitors hung on.
Conference League winners Crystal Palace made the step-up to Europe's second tier with aplomb, seeing off Lech Poznan 4-0 at Selhurst Park.
Palace made an impressive start to their debut in the competition by sweeping aside Polish champions Lech Poznan.
Yeremy Pino, Chris Richards and Jorgen Strand Larsen were on target in the first half before Eddie Nketiah fired a late fourth as Palace defied their disappointing Premier League form on a comfortable night at Selhurst Park.
Lech finished with 10 men after Radoslaw Murawski was sent off for a reckless bodycheck on Jaydee Canvot and moments later Nketiah put the finishing touch to a conclusive win.
Palace's first appearance in the Europa League came a year after they were kicked out of the competition due to a breach of multi-club ownership rules, with UEFA demoting them to the Conference League.
They duly won that, thereby securing their return to the Europa League, and they continued to show they taste for continental action against opponents who have made a strong start to their Polish title defence.
In Turin, Nick Woltemade scored his first Juventus goal in a 5-0 home success over NEC Nijmegen and received help from the opposition keeper.
Juventus are more used to the Champions League but the three-time UEFA Cup winners got off to a flyer.
NEC keeper Nikolas Polster charged out of goal and Nicolás González rounded him for the opener before Bosnian teenager Kerim Alajbegovic smashed home the second midway through the first half.
Germany forward Woltemade, a loan signing from Newcastle United, kicked off his Juve account with a penalty before the break. Zeki Çelik and Randal Kolo Muani added the second-half gloss.
Portuguese second-division side Torreense, the domestic Cup winners, won 2-1 at Norway's Lillestrøm and there was another away victory for Union Saint-Gilloise as they beat Viktoria Plzen 3-0.
Hoffenheim of Germany were earlier embarrassed 2-0 at OFI Crete despite having 57 per cent of the ball and 22 attempts to the Greeks' nine.
It was a party atmosphere in Heraklion given Crete are involved in major European competition for the first time since 2000.
Salzburg won 1-0 at Levski Sofia thanks to Haris Tabakovic's goal in the first period, while Besiktas beat Marseille 4-1 at home.
with agencies
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