Both dominated the opening sets, lost the middle tiebreakers and recovered in the third.
The fifth-seeded Tomic beat Potito Starace of Italy 6-1, 6-7 (4), 6-3 to make his first career quarterfinal on clay. Tomic was down a break of serve at the start of the final set before coming back.
Matosevic defeated fellow qualifier Robert Farah of Colombia 6-1, 6-7 (2), 6-2. Matosevic is playing his first career tournament on clay.