The Turkish club started slowly against its experienced opponent, conceding two goals in the first 16 minutes of the match at Jan Breydel Stadium.
In the hole on goals by Emmanuel Bonaventure and Stefano Denswil, Basaksehir recovered in the second half and equalized in a three minute-span, thanks to goals from Marcio Mossoro and new transfer Eljero Elia.
Basaksehir then went ahead in the 74th minute on another score by Mossoro.
Brugge, however, did not give up at its home turf and leveled the score 5 minutes later on a low free-kick by Denswil that beat goalkeeper Volkan Babacan.
The second leg of the qualifying round will be played Aug. 2 in Istanbul.
Basaksehir, which sold wonder kid Cengiz Under to Italian giant, Roma, for a fee of €13,40 million ($15.7 million), filled its squad with talent ahead of its Champions League tie.
In summer signings, the club added Eljero Elia from Feyenoord, Aurelien Chedjou from Galatasaray, Mevlut Erdinc from Hannover, Gael Clichy from Manchester City, Tunay Torun from Kasimpasa, and Gokhan Inler from Besiktas.
They also recently signed Kerim Frei from Birmingham City and Manuel da Costa from Olympiakos.