Gokhan Tore had fired the Turkish side in front 26 seconds into the second half, but Tom De Sutter slid in just after the hour mark to convert his team's first effort on target.
And a 79th-minute Lior Refaelov penalty ensured the hosts head into the second leg with a valuable advantage.
Tore's strike almost immediately after the restart sparked the game into life and Besiktas looked set to build on their victory as Demba Ba probed the home defence.
After a quiet opening eight minutes, there was a momentary delay when a rogue sprinkler broke rank to give the pitch a mid-match soak, but it was Club Brugge's joy that was dampened when De Sutter saw a 13th-minute goal ruled out.
De Sutter and Gulum clashed again moments later – this time the former earning a booking for a poorly judged tackle.
Having failed to trouble home stopper Mathew Ryan for the duration of the first half, Besiktas had the Australia international beaten almost immediately after the interval.
Besiktas certainly looked to have come to life after the break, with Ba trying his luck from distance on a couple of occasions
However, Club Brugge netted a leveller against the run of play when De Sutter slid in to divert Gedoz's low drive beyond Gonen.
Gonen then got down well to keep out a curling Laurens De Bock free-kick, but he was helpless to prevent Refaelov's spot-kick from nestling in the back of the net.
Having provided the assist for his side's opener, Gedoz - a half-time substitute - went down theatrically under the challenge of Serdar Kurtulus, with Refaelov making no mistake from 12 yards.
