The reigning champions looked set for a shock defeat after falling 2-1 behind despite Osimhen’s 53rd-minute opener.
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Alexandros Kyziridis equalised six minutes later before Jesus Ramirez put Corum ahead.
Kyziridis was then sent off in the 70th minute, leaving Galatasaray with a numerical advantage.
The pressure eventually paid off when Osimhen struck again in the 90th minute to rescue a point for the hosts.
The Nigeria international’s impressive start will further fuel speculation over his future.
Arsenal remain among his reported suitors, with The Telegraph reporting that his availability has been discussed alongside Galatasaray’s interest in Gabriel Martinelli and Ethan Nwaneri.