Rosenborg's late equaliser in a 1-1 draw with RB Leipzig cost the Bundesliga side second spot and instead gave the Scottish champions a reprieve as they advance behind Group B winners Salzburg.
All hope appeared lost for Celtic, who were outplayed for large stretches, after Munas Dabbur and Fredrik Gulbrandsen struck twice in 10 second-half minutes.
But the home fans were in boisterous sprits in the closing moments as news filtered through of the result in Germany and they had additional reason to cheer when Olivier Ntcham reduced the deficit in stoppage-time.
Socceroos midfielder Rogic played a full game in a boost to Australia coach Graham Arnold ahead of next month's AFC Asian Cup, but did come under scrutiny online.
The hosts rode their luck throughout the opening 45 minutes with Diadie Samassekou and Stefan Lainer both hitting the woodwork.
Dabbur, on target twice in the reverse encounter between these teams, finally made Salzburg's dominance count by heading in Lainer's cross in the 67th minute.
Craig Gordon gifted away a second 10 minutes later as Gulbrandsen stole the ball from the goalkeeper's throw and tucked into an empty net, but the blow was softened by Rosenborg's unexpected late goal against Leipzig.
Jerome Onguene then fouled Filip Benkovic deep into stoppage-time and Ntcham was able to add a footnote to a strange match from the spot, the midfielder pouncing on the rebound of Alexander Walke's save from his initial attempt.
Meanwhile Rogic's Socceroos teammate Vukovic also played a full game as his Genk outfit topped Group I after thrashing Sarpsborg 4-0.
Genk finished the group stage with just one loss in their home and away clashes against Malmo, Besiktas and Sarpsborg respectively.
Elsewhere, Australia striker Apostolos Giannou played 84 minutes in Larnaca's heavy 5-1 loss to Bayer Leverkusen with the Cyprus-based club finishing third in Group A.
And finally, Socceroos defender Alex Gersbach was an unused substitute as Rosenborg secured a 1-1 draw against RB Leipzig to knock the Germans out of the Europa League.
The result secured Aussie teammate Rogic and Celtic's passage through, despite their home defeat.
