The Penguins opened a four-game homestand with their sixth straight victory, the longest current winning streak in the NHL.
Phoenix failed in its bid to move in front by itself at the top of the Pacific Division. The Coyotes are tied with Dallas for the division lead, the Stars having won two more games than Phoenix.
Fleury protected the 2-0 lead until Ray Whitney tallied 1:27 into the third period.
Phoenix went 11-0-1 in February, but has lost its first three games in March.
Mike Smith stopped 26 shots for the Coyotes.
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