Gulbis managed just two breaks on the day with the second leading to a deciding tiebreaker and 6-3, 3-6, 7-6 (7-3) decision over Jeremy Chardy in a match that took nearly 2 1/2 hours.
Both players served well, taking about two-thirds of the points on serve but Gulbis made the most of his break chances, winning both his opportunities. Gulbis fought off 10 of the 12 break points Chardy had, going 6-for-7 in that statistic in the third set.
No. 7-seeded Grigor Dimitrov took out Marius Copil 6-3, 6-4 without dropping serve, although he had to save six break points to do that.
Jan-Lennard Struff raced past Milos Sekulic 6-3, 6-0 in 52 minutes. He lost 10 points overall in the second set.
Also Tuesday in other first-round matches, Jack Sock was a 6-4, 6-2 winner over Bernard Tomic; Guillermo Garcia-Lopez defeated Nils Langer 7-6 (7-5), 6-3; and qualifier Joachim Johansson, in a 54-minute match, eliminated Alejandro Falla 6-1, 6-3.
Celebrity Families of 2014 [PHOTOS]