Joffrey Lupul scored twice and Dan Sexton added a goal as the Ducks scored three times in a 9:51 span of the third period to force overtime.
Sbisa's goal came with Anaheim (2-1) on a two-man advantage after two Phoenix penalties, one in the final seconds of regulation.
Peter Mueller, Jeff Hoggan and Jim Vandermeer scored their second goals of the preseason for the Coyotes (1-2-1).
Phoenix outshot the Ducks 46-21 overall and 38-6 in the first two periods.
Coyotes coach Wayne Gretzky, whose $8.5 million contract for 2009-10 is part of a bankruptcy dispute being adjudicated in a Phoenix court, missed his fourth straight game. Associate coach Ulf Samuelsson ran the team.
Mueller scored on a slap shot from just inside the blue line on a power play to give the Coyotes a 1-0 lead with 9:03 remaining in the first period.
Hoggan made it 2-0 53 seconds later, when he beat Timo Peilmeier to the far corner from the right circle.
Phoenix outshot Anaheim 30-2 in the first period, and the final Ducks' shot came from center ice as time expired.
Vandermeer scored from outside the right circle to give Phoenix a 3-0 lead with 18 seconds remaining in the second when new goalie Jean-Philippe Levasseur was screened by Brett MacLean.
Lupul scored Anaheim's first goal on a power play with 9:51 remaining during a 5-minute major and a game misconduct penalty on defenseman Francis Lessard.
Sexton scored with 7:00 remaining to make it 3-2, and Lupul tied it with 1:10 left. All the scoring came off backup goalie Josh Tordjman, who replaced Al Montoya to start the third period.