Johan Elmander and Albert Riera were included in the Galatasaray starting lineup, as was former Arsenal favourite Emmanuel Eboue, while Wesley Sneijder and Drogba began the afternoon among the substitutes.
Sanogo almost had a dream start in front of the home crowd when Felipe Melo gifted him the ball, but the 20-year-old's low effort was palmed away.
The 24-year-old's wayward cross evaded everybody, including Muslera, and looped into the far corner.
Galatasaray introduced both Drogba and Sneijder after the half-time break, but the Ivorian lambasted first Nordin Amrabat and then Emre Colak as his teammates wasted good chances with the 35-year-old well placed on both occasions.
Drogba took matters into his own hands after he was bundled over by Ignasi Miquel by slotting the resulting penalty into the corner to level the scores.
With just four minutes remaining, Drogba - who tormented Arsenal throughout his career at Chelsea - once again had the last laugh as he collected Sneijder's pass and smashed the ball beyond a helpless Wojciech Szczesny.
The turnaround by the Turkish outfit saw them leave London as winners of the Emirates Cup.