Spain's Montanes quickly dispatched Romanian Adrian Ungur 6-4, 6-2, gaining the second round, while compatriot Granollers needed a first-set tiebreaker to vanquish Croatian wild card Mate Pavic 7-6 (7-2), 6-2.
Granollers will next face Argentina's Horacio Zeballos, who bested Austrian qualifier Martin Fischer 7-5, 1-6, 6-3.
Also advancing was fellow Argentine Leonardo Mayer, who downed Frenchman Kenny De Schepper 6-4, 6-4, next drawing top seed and 2012 runner-up Phillip Kohlschreiber of Germany.
Other Day 1 winners in Kitzbuhel included Austrian wild card Dominic Thiem and Spaniard Daniel Gimeno-Traver.
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