French-born Mali forward Marega struck four minutes after the break as Porto claimed their first win in Group D, leaving the Portuguese champions level on points at the top with Schalke and one ahead of their Turkish opponents.
Both teams created chances in an open end-to-end game with both Casillas and his opposite number Fernando Muslera keeping the score down.
Muslera was first to be called into action when the Uruguayan got down to block Yacine Brahimi's powerful volley at the foot of the post, a chance created by Jesus Corona's weaving run.
Former Real Madrid goalkeeper Casillas, taking part in his 20th Champions League campaign, made two important saves with his legs just before halftime.
First, he blocked Yuto Nagatomo's close-range effort, then he foiled Sinan Gumus after the Galatasaray forward had burst from inside his own half.
Porto, beaten 5-0 by Liverpool in their last home game in the competition, broke through when Alex Telles swung over a cross and Danilo distracted three defenders leaving Marega unmarked to head home from close range.
Garry Rodrigues missed a chance to level by firing over after a one-two with Gumus and Muslera denied Marega a second goal after the Porto forward broke clear of the Galatasaray defence.
(Reporting by Brian Homewood; Editing by Toby Davis)
