Atiba and Larin gave a 2-0 lead to Besiktas in the first half at the Vodafone Park.
In the second half, Vincent Aboubakar made the score 3-0 and the away team was reduced to 10 men when Mehmet Topal picked up a second yellow card in the 70th minute.
Despite the sending off, Fredrik Gulbrandsen scored twice for the visitors but Basaksehir could not complete come back and the game ended 3-2.
Following this defeat, Basaksehir's 4-match winning run ended while Besiktas increased their points to 13 to catch up with Basaksehir on the table.
Results of Saturday's Super Lig matches:
Yukatel Denizlispor - Gaziantep FK: 0-1
Fatih Karagumruk - Sivasspor: 1-1
Genclerbirligi - Fenerbahce : 1-5
Besiktas - Medipol Basaksehir: 3-2
