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Vince Dunn and Adam Larsson also scored.
Philipp Grubauer stopped 27 shots for the Kraken.
Seattle sent infielder Ben Williamson to the Rays, and a pair of minor league prospects to the rebuilding Cardinals.
Suárez was the top slugger left on the free agent market and the two-time All-Star returns to Cincinnati, where he played seven seasons.
Eeli Tolvanen and Jared McCann scored in the first period for the Kraken and Joey Daccord made 27 saves.
Brandon Montour and Matty Beniers also scored for the Kraken.
Jordan Eberle and Matty Beniers each added a goal and an assist.
Seattle lost their most recent appearance to New England, its opponent in two weeks at Levi’s Stadium in Santa Clara, California.
Matty Beniers and Kaapo Kakko also scored goals for Seattle, while Philipp Grubauer had 24 saves.
Joey Daccord made 26 saves for Seattle.