Vokoun, who left the Panthers as a free agent after last season and signed a one-year, $1.5 million deal with the Capitals, stopped nine shots in each of the final two frames to record his 45th career shutout.
Marcus Johansson and Alexander Semin tallied while Jason Chimera added an empty-netter for Washington, which began the season with five straight wins for the first time in franchise history.
Rookie netminder Jacob Markstrom turned aside 29 shots for the Panthers in his first NHL start.
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