The second-seeded German moved to 50-16 in a season that has brought three titles, including the Madrid Masters.
Zverev converted all four of his break points while saving eight of the 10 held by the 47th-ranked Dutchman.
Haase used a between-the-legs lob to force a break in the second set that Zverev retrieved with his own 'tweener into the net.
Third-seeded Marin Cilic now has a 1-3 record in October after losing 7-5, 7-6 (2) to the 93rd-ranked Marius Copil of Romania in a second-round match.
Taylor Fritz of the United States joined Copil in the quarterfinals by beating Swiss wild-card entry Henri Laaksonen 6-2, 7-5.
Also in the first round Wednesday, fourth-seeded Stefanos Tsitsipas reached the 40-win mark in beating Jeremy Chardy 6-2, 7-6 (3). Tsitsipas came to Basel from winning his first career title in Stockholm on Sunday.
Jack Sock, the fifth-seeded American, was eliminated by Ernests Gulbis, 7-5, 6-4. Gulbis also beat Sock in the Stockholm quarterfinals last week.
Roberto Bautista Agut, the eighth-seeded Spaniard, advanced to the second round by beating Joao Sousa 6-4, 6-3.
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