The Coyotes snapped a two-game losing streak to start the season (0-1-1) and spoiled the Predators' home opener by dealing them their first loss in three games.
Schlemko scored at the 12-minute mark with a sharp-angle shot from the far side of the left circle after Petteri Nokelainen's initial try was deflected in front.
The puck skipped out to Schlemko, who snapped a quick try on net as Rinne failed to scramble back in time, sparking an offensive outburst for the Coyotes
Rinne was too slow on Whitney's one-timer from high on the left side just 2:28 later, and Korpikoski made it 3-0 with a goal at 18:45, beating the Predators goaltender from the slot after Boyd Gordon spun to find him with a pass.
Boedker pushed the lead to 4-0 at 11:26 of the second period, controlling a loose puck in front before stuffing it home.
Suter finally got the Predators on the board while teammate Jordin Tootoo was off on a slashing penalty.
From high on the right side, he blasted a slap shot through Matt Halischuk's screen in front of LaBarbera, who reacted too late with his glove as the puck sailed past him.
Wilson scored on a slap shot from the left side at 9:08 of the third period and Doan's empty netter came with 70 seconds remaining.
The Coyotes played their third straight road game to open the season, but are headed home for three games starting Saturday against Winnipeg...The Predators remain at home to play New Jersey on Saturday, then go on the road for three straight games.