The seventh-seeded Spaniard struggled with his serve early, dropping the first set and trailing 3-1 in the second, but his form picked up and he broke the 121st-ranked Donskoy twice to even the match at one set apiece.
Garcia-Lopez broke decisively in the fourth game of the third set and finished the match by serving out to love.
In other first-round action, Italy's Flavio Cipolla advanced with a 7-6 (4), 7-6 (6) win over qualifier Andrei Vasilevski of Belarus, and Rajeev Ram of the United States beat Matthias Bachinger of Germany 6-4, 6-4.
Ram broke Bachinger early in the first set but fell 4-1 down in the second before winning five consecutive games.
Mikhail Youzhny, the 2004 champion and a two-time runner-up, is the top-seeded player in the 18th edition of the tournament.