Basaksehir crushed Wolfsberger 3-0 at the Graz Liebenau stadium in the Europa League on Thursday to go top of Group J.
The visitors had to wait until the 73rd minute to take the lead when Edin Visca converted a penalty effort.
The penalty also saw the home side reduced to 10 men after Rnic was sent off for giving away the spot kick.
Enzo Crivelli netted a brace with goals on 84 and 87 minutes to wrap up a memorable away European competition win for the Istanbul minnows.
The win moved Basaksehir top of Group J on seven points.
The Super Lig outfit are two points clear of Roma and Borussia Monchengladbach who are tied on five points.
The defeat saw Wolfsberger sink to the bottom of the table on four points.
Basaksehir will take on Roma next in Istanbul. The Serie A outfit suffered a 2-1 defeat against German side Monchengladbach in the other group game.
Wolfsberger 0-3 Basaksehir
Stadium: Graz Liebenau
Referee: Sandro Scharer, Stephane De Almeida, Bekim Zogaj (İsviçre)
Wolfsberger: Kofler, Novak, Sollbauer, Rnic, Schmitz, Schmid, Leitgeb (min. 88 Gollner), Ritzmaier, Liendl, Weissman, Niangbo (min. 81 Schmidt)
Medipol Başakşehir: Mert Günok, Caiçara, Ponck, Skrtel, Clichy, Mehmet Topal, Berkay Özcan (min. 80 Arda Turan), Azubuike (min. 89 Elia), Visca, Gulbrandsen (min. 88 Aziz Eraltay), Crivelli
Goals: min. 73 Visca (Penalty), min. 84 & 87 Crivelli (Medipol Başakşehir)
Red Card: min. 72 Rnic (Wolfsberger)