The only seeded players in action on the opening day, No. 7 Montanes served eight aces in defeating Adrian Ungur of Romania 6-4, 6-2, and No. 8 Granollers beat Mate Pavic of Croatia 7-6 (2), 6-2.
Granollers, who saved all six break points against his serve, will next play Horacio Zeballos of Argentina, who beat Martin Fischer of Austria 7-5, 1-6, 6-3.
Also, Leonardo Mayer of Argentina defeated Kenny De Schepper of France 6-4, 6-4 to set up a second-round match against top-seeded Philipp Kohlschreiber of Germany.
The top four seeds have a bye in the opening round.
Results from the ATP Kitzbuehel Cup on (x denotes seeding):
Dominic Thiem (AUT) bt Andrey Kuznetsov (RUS) 6-2, 7-5
Daniel Gimeno (ESP) bt Antonio Veic (CRO) 6-1, 6-3
Horacio Zeballos (ARG) bt Martin Fischer (AUT) 7-5, 1-6, 6-3
Leonardo Mayer (ARG) bt Kenny De Schepper (FRA) 6-4, 6-4
Marcel Granollers (ESP x8) bt Mate Pavic (CRO) 7-6 (7/2), 6-2
Albert Montanes (ESP x7) bt Adrian Ungur (ROM) 6-4, 6-2