Vukovic made a number of key saves as his Genk side hung on to claim a draw on the road against a Slavia side, which has yet to lose a Europa League clash at home this season.
Genk was on the back foot early in the contest as Slavia midfielder Miroslav Stoch fired over the bar in the fifth minute.
It set the tone for the match and Vukovic was lucky to avoid conceding an early goal as Milan Skoda hit the post in the 19th minute.
Genk had their own near miss soon after as Leandro Tossard also fired against the woodwork.
Slavia upped the tempo in the second stanza but Vukovic was up to the task, making saves in the 57th and 64th minutes to deny solid efforts from Skoda.
The former Sydney FC shot stopper made two more saves late as Slavia struggled to make the most of their chances.
Genk clung on in the dying stages to claim a draw. The Belgians will host the return leg next Friday (AEDT) March 22.