Early goals from Sneijder and Aurelien Chedjou saw Galatasaray cruising but it was brought crashing back to earth just before half-time as Kayserispor netted twice in 60 seconds, Pablo Mouche's 44th-minute penalty making it 2-1 and Jakson levelling soon after.
Gala regrouped at the break though and retook the lead through Burak Yilmaz's 57th-minute strike before Drogba sealed the win 16 minutes from time as Roberto Mancini's men kept in sight of Fener, which won on Friday night.
Eskisehirspor was also among the goals as it climbed to fifth with a 4-1 win over Caykur Rizespor.
All five goals came during a 28-minute spell in the second half with Cristobal Jorquera (52), Erman Kilic (71), Erkan Zengin (75) and Alfred N'Diaye (80) on the mark for the victor, with Leonard Kweuke having briefly drawn Caykur level with a 69th-minute equaliser.
In Sunday's other game, Ferhat Kiraz's 66th-minute goal earned Bursaspor a 1-0 win at Konyaspor.