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.
De Sutter had earlier seen a goal disallowed during a first half that offered little by way of entertainment.
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.
However, De Sutter restored parity in the 62nd minute before Felipe Gedoz was felled in the box to present Refaelov with the chance to snare victory.
The Israel international duly dispatched into the bottom right-hand corner to earn the home side a hard-fought win.
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.
The attacker headed in from a corner, only to see his effort chalked off for taking out Ersan Gulum as he looked to make contact with the ball.
De Sutter and Gulum clashed again moments later – this time the former earning a booking for a poorly judged tackle.
Goalscoring opportunities were at a premium during a cagey first half, but another incident involving De Sutter and Gulum led to a glorious chance for Club Brugge to break the deadlock.
This time it was De Sutter on the receiving end of a clumsy Gulum challenge, but Davy De Fauw could not turn the ball in after goalkeeper Cenk Gonen had struggled to deal with the resulting free-kick.
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.
Tore picked up the ball on the edge of the box before dancing his way through a series of defenders to rifle a left-footed strike beyond Ryan.
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.
Refaelov could have made it 3-1 in the closing stages, but directed his header just over the crossbar.
