The striker assisted Yunus Akgun for the opening goal after nine minutes, but the hosts responded strongly, scoring four times to claim all three points.
The result allowed Istanbul rivals Fenerbahce to close the gap at the top of the table to four points after their 3-1 win over Istanbul Basaksehir.
Osimhen has now apologised to Galatasaray fans, admitting the performance fell below expectations.
“We knew it wouldn’t be easy. We knew our opponent was tough and that winning the championship here wouldn’t be easy. We have to congratulate our opponent. They pushed us hard. To be honest, we can’t say we played well either,” Osimhen told the club’s official website.
“Now we’ll focus on our home game. Hopefully, we’ll win there and declare our championship. We apologize to our fans who supported us so well away from home. They didn’t leave us alone for 90 minutes. Now we’ll look ahead. We’ll focus on the next game. We want to celebrate the championship in that game.”