Zetterberg -- who has scored a goal in six straight games -- leads the NHL with 17 points and has scored at least one point in each of his nine games in the new season.
Dominik Hasek made 19 saves on 21 shots for Detroit.
Detroit opened the scoring when Hudler scored his first goal of the season at 4:37 of the first period. The Coyotes tied it at 12:45 when Reinprecht scored on a feed from Peter Mueller -- and then went up, 2-1, when Morris scored at 17:15.
Maltby tied it, 2-2, with 8:34 left in the second, and then scored the decisive goal with 26 seconds remaining in the second.
Celebrity Breakups and divorces of 2014 [PHOTOS]