Serie A giants Inter lost 2-0 to Croatia's Hajduk Split at the San Siro, only surviving courtesy of their 3-0 win in the away leg last week.
Inter had a flurry of chances just before the break but fell further behind when Vukovic rifled the ball home from just inside the area in the 68th minute.
Vukusic nearly sent the game to extra time when his low shot was just wide of the post as Inter fans watched in stunned silence.
"It's only August 9, these things happen," said Inter coach Andrea Stramaccioni. "The important thing is that we got through."
Athletic Bilbao, last season's runners-up, also qualified despite losing to Croatian opponents as they went down 2-1 at Slaven Belupo Koprivnica but won 4-3 on aggregate.
SPL side Dundee United were overpowered 5-0 by Dinamo Moscow to bow out of the competition 7-2.
Steve McClaren's FC Twente made it safely through to the play-off round, beating Czech side Mlada Boleslav 2-0 in both legs.
However, fellow Dutch side Vitesse Arnhem went out 4-0 on aggregate to big-spending Anzhi Makachkala.
On a night of few shocks, the other big names to go through included Marseille, Sparta Prague, Steaua Bucharest and Red Star Belgrade.