The former Chelsea star replaced Umut Bulut in the 63rd minute before heading in his team’s opening goal just five minutes later.
Buruk Yilmaz made it 2-0 in the 70th minute with Sertan Vardar cutting the deficit with five minutes left.
Galatasaray now have an eight-point lead over Besiktas at the top of the Turkish first division.
Ivory Coast striker Drogba, 34, signed an 18-month contract with top-flight Galatasaray at the end of January but Shanghai Shenhua, with whom he signed on a two-and-a-half year deal in June last year, opposed the move.
He is being paid 10 million euros ($13.5 million) to play in Turkey with a bonus of 15,000 euros for every match played.
Galatasary are due to play German side Schalke 04 next Wednesday in the last 16 of the Champions League.
Drogba — a Champions League winner with English Premier League club Chelsea last season — is looking to relaunch his career in Europe and play at a higher standard than in China, with a view to being at the next World Cup in Brazil in 2014.