Mike Johnson added an empty-net goal with 10 seconds remaining as the Coyotes moved into a tie with Los Angeles for 10th in the Western Conference, five points behind eighth-place Edmonton.
Phoenix is 6-1-1 in its recent run, with Burke winning two of the last three.
Sandis Ozolinsh scored for the Ducks, who were 2-0-1 against the Coyotes this season and outscored them 9-4 in three games at Anaheim.
SABRES 5, STARS 3
At Buffalo, N.Y., Curtis Brown scored the go-ahead goal midway through the third period to lift the Sabres.
Ales Kotalik, Jason Botterill and Stu Barnes had a goal and an assist each, Brian Campbell scored a goal and Miroslav Satan had three assists for Buffalo.
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