Karel Vejmelka made 30 saves for Arizona in its second straight loss. The Coyotes visit St. Louis on Thursday night and then play their home opener Saturday against Anaheim.
Barzal connected on a one-timer at 3:47 shortly after Coyotes forward Barret Hayton was penalized for slashing Simon Holmstrom, preventing a scoring opportunity for New York.
Sorokin signed a contract extension this summer after supplanting Semyon Varlamov as the Islanders’ starting goalie. The 28-year-old goaltender has three shutouts against the Coyotes and 17 overall for his career.
The Coyotes struggled to establish a presence in the offensive zone and only generated seven shots on goal through the first two periods.
The Islanders won two consecutive games to start a season for the first time since 2014-15 when they began the season with four straight victories.
Coyotes: Visit the Blues on Thursday.
Islanders: Host the New Jersey Devils on Friday.