The Ivory Coast frontman - who left Chelsea after spearheading their 2012 Champions League final victory before a short stint with Shanghai Shenhua in China - converted a soft penalty on 78 minutes before then producing a crisp finish as the Turks secured their second victory of the weekend tournament, having fallen behind to Theo Walcott's first-half curling effort.
Arsenal, who are still chasing a deal for wantaway Liverpool striker Luis Suarez, showed good form in patches, but again had no answer to the 35-year-old, who had been on Arsene Wenger's radar as a youngster at Guingamp.
Arsenal's only summer signing Yaya Sanogo, a free transfer from Auxerre, was handed a start in attack, while Spain midfielder Santi Cazorla was back in action after extra time off following the Confederations Cup.
There was an early chance for France Under-21 striker Sanogo to become an instant cult hero when he collected a loose pass on the edge of the penalty area, but his angled shot was saved by Fernando Muslera.
Arsenal, who came from 2-0 down to draw with Rafa Benitez's Napoli on Saturday, continued to press and had a penalty shout turned down after Aaron Ramsey tumbled.
On 18 minutes, Walcott expertly took down a long ball from the Welshman into the Galatasaray box, but could then only flick it over the keeper and wide.
Former Bolton forward Johan Elmander caused Arsenal some concern with his link-up play, but Arsenal goalkeeper Wojciech Szczesny, making his first appearance of pre-season after injury, was not really tested.
Arsenal took the lead five minutes before half-time when Walcott's curling cross from the left bounced through the six-yard box and dropped into the far corner.
Drogba was introduced for the second half - to some jeers from the home fans, who remembered him as so often Arsenal's tormentor during his time with Chelsea. Dutch international Wesley Sneijder also came on.
Drogba was straight into the action, fashioning a chance when he turned Per Mertesacker just outside the Arsenal penalty area, but his shot was straight at Szczesny.
Arsenal, who made several expected substitutions, continued to look sharp, with Alex Oxlade-Chamberlain looking to have been tripped in the penalty area before a downward header from Olivier Giroud was well saved.
The Turks threatened also as Szczesny beat away a fierce drive from Sneijder.
Galatasaray were awarded a penalty on 78 minutes by referee Jon Moss when substitute Ignasi Miquel was adjudged to have pushed over Drogba, with contact looking minimal at best.
The former Chelsea man made no mistake from 12 yards to continue his fine scoring form against the Gunners.
Drogba then won it for Galatasaray when he collected a cross-field ball from Sneijder before cutting inside Mertesacker and drilling his shot past the Arsenal keeper.
Arsenal must now regroup for next weekend's final pre-season friendly against Manchester City in Helsinki, before the action kicks off for real with the visit of Aston Villa on August 17.