The 68th-ranked Dutchman was a break up in the second set but lost his lead before converting his second match point in the tiebreaker.
He finished with 10 aces.
Haase, who won the event in 2011 and '12 and reached his third career final in Gstaad last weekend, will next play Daniel Brands.
The German beat fifth-seeded Carlos Berlocq of Argentina 7-6 (4), 2-6, 6-2.
Also, Victor Hanescu of Romania defeated Aljaz Bedene of Slovenia 6-2, 6-1, and Jan Hajek of the Czech Republic ousted Aldin Setkic of Bosnia by the same score.
Results from the third day of the ATP Kitzbuehel Cup (x denotes seeding):
Leonardo Mayer (ARG) bt Philipp Kohlschreiber (GER x1) 6-4, 7-6 (7/4)
Marcel Granollers (ESP x8) bt Horacio Zeballos (ARG) 6-0, 2-0 retired injured
Guillermo Garcia-Lopez (ESP) bt Thomaz Belluci (BRA) 6-7 (1/7), 6-3, 7-6 (7/4)
Robin Haase (NED) bt Guillaume Rufin (FRA) 6-4, 7-6 (7/4)
Daniel Brands (GER) bt Carlos Berlocq (ARG x5) 7-6 (7/4), 2-6, 6-2
Victor Hanescu (ROM) bt Aljaz Bedene (SLO) 6-2, 6-1
Jan Hajek (CZE) bt Aldin Setkic (BIH) 6-2, 6-1
Andreas Haider-Maurer (AUT) bt Dennis Novak (AUT) 6-4, 6-4