Greiss, who joined the Coyotes this year after spending the first four seasons of his career with San Jose, made seven saves in relief of Mike Smith during a one-sided loss to the New York Islanders on Tuesday.
In his Phoenix debut as a starter, he allowed only a goal to Maxime Talbot late in the second period that brought about a 1-1 tie.
Oliver Edman-Larsson then scored with just 13 seconds to go in the middle stanza and that stood up as the winning goal.
With this victory, Greiss equaled his entire win total from last season.
Rob Klinkhammer scored the first Phoenix goal as part of the Coyotes' second straight win.
Steve Mason made 29 saves in the loss.
Boston schools pull out free condoms over wrapping complaints
Ray Liotta sues skin care company over use of likeness