Umut Bulut gave the hosts an early lead before the former Arsenal man levelled matters in the 39th minute to see Abdullah Avci’s side hold on for a point.
The goal was the 33-year-old striker’s eighth in 12 Turkish top-flight encounter for his side.
The Fatih Terim Stadium outfit are second in the log after garnering 27 points - two adrift leaders Galatasaray - from 13 games.
Adebayor will hope to take his form into the Turkish Cup when Basaksehir play Kahramanmaraşspor in a fifth round tie on Thursday.
