Both matches were delayed second-round encounters, and for 18-year-old qualifier Tomic the victory represented a significant first.
The Australian said: “It’s the first time I’ve been down in my career two sets to love and a break, and potentially a double break down.
“I think I gave it a shot. I tested myself to win that match, to get back in that third set, and I did.”
Tomic next faces fifth seed Robin Soderling, who fought back from two sets down himself on Thursday to defeat another Australian, former champion Lleyton Hewitt.
Tomic said: “Hopefully he’s not going to like the way I play. But he can hit you off the court, as he’s done the last few years. He’s beaten a lot of guys very easily.”
Eleventh seed Jurgen Melzer completed the third-round line-up by seeing off Dmitry Tursunov 6-3 2-6 7-6 (7/5) 7-6 (7/1), while Richard Gasquet reached the fourth round thanks to a 6-3 6-2 6-4 victory over Simone Bolelli.