France's Paire fell victim to Italian Paolo Lorenzi 6-4, 6-4 in Day 2 action indoors at Wiener Stadthalle.
Belgium's Malisse similarly was shown an early exit as Slovenian qualifier Grega Zemlja used a third-set tiebreaker to triumph 4-6, 6-1, 7-6 (8-6).
Also in the first round, American Jesse Levine dispatched Poland's Lukasz Kubot 6-3, 6-4, and 2010 Vienna finalist Andreas Haider-Maurer of Austria was sent packing by Canadian qualifier Vasek Pospisil 3-6, 7-6 (7-3), 6-1.
Other Tuesday winners included Slovenian Aljaz Bedene, Australia's Matthew Ebden and German qualifier Daniel Brands.
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