Jordan Martinook and Michael Bunting scored goals for Arizona, and goalie Louis Domingue stopped 33 of 36 shots.
Martinook, who scored nine goals in 2015-16 in his first rookie season, gave the Coyotes a 1-0 lead by scoring a goal off a feed from Conor Garland at 8:45 of the first period.
Ryan Carpenter scored for San Jose at 11:81 of the second period, but the Coyotes re-took the lead just 35 seconds later thanks to a goal by Bunting, his second of the preseason.
Tomas Hertl scored a goal at 7:11 of the third period to even the score 2-2.
Jakob Chychrun, a defenseman whom the Coyotes picked 16th overall at this year's draft, led Arizona in ice time at 24:12.
The Coyotes next play on Saturday night at Gila River Arena. The puck drops at 6 p.m. Arizona time. The game can be heard on KTAR News 92.3 FM or seen via live stream at ArizonaCoyotes.com.