The Lions overwhelmed their opponents from the start with the support of 30,000 fans at the Turk Telekom Stadium, scoring their first goal in the 15th minute.
Gary Rodrigues' speedy cross found Tolga Cigerci in the six-yard box, giving the team a 1-0 lead.
But Galatasaray conceded a corner goal, with Kayserispor’s Levent Gulen scoring the header and equalizing in the 29th minute.
Yet the Istanbul club saw a good series of passing from their new transfers Mariano, Batefimbi Gomis and Younes Belhanda, who calmly finished inside the penalty area and put his team back up again in the 35th minute.
The momentum continued, with Belhanda assisting Gomis, who minutes later scored a low-driven powerful shot to the jubilation of Galatasaray fans.
The second half was all about Galatasaray maintaining control of the match, with Gomis scoring in the dying minutes.
The score cemented Galatasaray’s lead in the standings.
Earlier in the day, the club announced the transfer of Algerian right winger Sofiane Feghouli from English club West Ham United.