Meanwhile, World Cup star Nestory Irankunda's hopes of making his debut in club football's biggest tournament on Wednesday will have to wait as he had to watch from the bench as his Portuguese side Sporting kicked off their challenge with a 3-1 win over Turkey's Galatasaray.
Twice-capped Stensness, the one-time Central Coast Mariners defensive midfielder who's become a cult figure for his Scandinavian side, was a central figure in Viking getting into group stages of the world's biggest club tournament for the first time, an achievement he'd happily dubbed as "crazy".
But Viking's excitement at making their big-time bow at their Bundesliga hosts quickly began to evaporate in just 12 first-half minutes thanks to the first hat-trick of this season's tournament from Ermedin Demirovic.
The German-born Bosnian international struck in the 20th, 26th and 32nd minutes to put Stuttgart in control, even after Viking's Croatian-born captain Zlatko Tripic had equalised two minutes after Demirovic's opener.
It was the first treble of the 2026-27 event after eight hat-tricks had been scored last season, including two by Real Madrid's Kylian Mbappe.
"For me personally it was the perfect start and also for the team as a whole," beamed Demirovic, who'd not managed to score for Bosnia-Herzegovina in the World Cup.
Four Australian players have made it into the group stages of the latest edition of the Champions League, with Stensness and currently injured striker Nick D'Agostino both in Viking's squad.
Jordy Bos is also out of action, still recovering after knee surgery, and is unlikely to feature for Dutch former European champions Feyenoord in the group stages in forthcoming weeks. They were hammered 5-1 at Barcelona on Wednesday.
Irankunda, Sporting's 15 million euro signing from English side Watford, will have hoped to have been thrown into the fray in front of 44,000 fans at the Jose Alvalade stadium.
Yet the exciting Socceroo was not among the five subs brought on as the hosts recovered from an early own goal from captain Goncalo Inacio to win with goals from Geny Catamo, Luis Suarez, from the penalty spot, and Rodrigo Zalazar.