Sevilla eliminated the Istanbul side on a 4-3 aggregate score after Basaksehir midfielder Emre Belozoglu's 90th minute free-kick came off the woodwork, costing the club what would have been a memorable away victory at the Ramon Sanchez Pizjuan stadium.
Basaksehir started the match at a fast pace, finding the net in the 17th minute from first-leg scorer Eljero Elia. The Dutch winger slid in Junior Caicara's low ball to give Basaksehir the lead.
The second half was to be a different story, as Sevilla equalized and gained the upper hand when Sergio Escuredo brushed aside his marker to score a header in the 52nd minute.
The La Liga side then took a commanding lead in the 75th minute with Wissam Ben Yedder's low driven shot beating Basaksehir goalkeeper Volkan Babacan after a counter-attack.
Basaksehir increased their tempo in the last 10 minutes before Edin Visca restored the Istanbul club's morale when he crashed home a powerful shot in the 82nd minute.
But Basaksehir’s last-minute heroics were not enough as Sevilla managed to draw 2-2 and move on to the group stages.
Basaksehir will continue their European campaign in the UEFA Europa League. Both competitions' draws will be made in Monaco on Thursday.