Besiktas were back in familiar territory, where they have gone unbeaten in their six games at home this season, winning five of those.
However, it was visitors Lugano that got off to a better start, despite going into the game as heavy underdogs. Zan Celar was slipped through on goal in the third minute, but the striker lacked composure as his early effort drifted well wide.
From then on, the Turkish outfit took control of proceedings, having the lion's share of possession, but they still struggled to break the Swiss defence down, with chances coming at a premium.
Rachid Ghezzal was looking the most threatening for Besiktas, as the Algerian saw a powerful shot from outside of the box palmed away. But the winger continued to probe and he produced a pinpoint assist for the opening goal.
Running down the right flank, Ghezzal whipped a fantastic delivery into the box, to which Vincent Aboubakar met with an impressive diving header into the bottom corner, giving the Turkish side the lead going into half time.
The Black Eagles began the second half on the front foot as they looked to put the tie to bed with an early second goal, and it duly arrived in the 52nd minute.
Aboubakar collected a loose pass in the Lugano half, went on a mazy run into the box and slotted a clinical finish past Amir Saipi.
Besiktas were cruising up until the hour mark, but that narrative soon changed and the Turkish side went into defensive mode, trying to protect their lead as they were reduced to 10 men.
Valentin Rosier was shown a second yellow card, which gave Swiss side Lugano renewed hope, as they pushed forward to try and pull a goal back.
With a man advantage, Lugano began to see more of the ball and they made their pressure pay with a stunning comeback in the final 10 minutes.
Ignacio Aliseda pounced on a loose ball in the box to fire home and set up a tense finish.
Just minutes later, the Swiss outfit netted a second to level the scoreline as Renato Steffen did well to steer home after Allan Arigoni clipped a ball into the box.
The comeback was then sensationally completed in the 90th minute when Eric Bailly inadvertently directed a shot into his own net despite the ball initially going off target, handing Lugano a first-ever win in the Conference League.
Flashscore Man of the Match: Vincent Aboubakar (Besiktas)
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Other Europa Conference League results (18:45 CET kick-offs)
Group A
Olimpia Ljubljana 0 Slovan Bratislava 1
Group B
Group C
FC Astana 1 Viktoria Plzen 2 (16:30 CET kick-off)