The Spaniard, following a 5-under-par 67, and Drysdale, who shot 65, were at 13-under 131 at the Centro Nacional course.
Drysdale, of Scotland, is looking for his first title on the tour.
Ireland's Gary Murphy (65), Italy's Emanuele Canonica (65) and Ross McGowan (66) of England were tied for third place at 132 and Jorge Camillo (66) of Spain and Englishmen Danny Willett (67) and Anthony Wall (67) came in at 133.
Garcia said he was glad to hear during his round that golf had been added to the Olympics for 2016 and 2020.
"This is a very special day," Garcia, 29, said. "We've been fighting for a year now to get it in and it feels good. It's going to be an amazing experience for all of us."