Dany Heatley also scored for Ottawa -- which won for the first time in four games and remained two points behind the first-place Montreal Canadiens in the Northeast Division. Montreal beat Los Angeles 5-2 Saturday.
Martin Gerber made 33 saves on 35 shots for the Senators.
Craig Weller and Peter Mueller scored and Ilya Bryzgalov surrendered four goals on 32 shots for Phoenix, which has lost two straight and is still five points behind Vancouver and Nashville for the eighth and final playoff berth in the Western Conference.
Phoenix scored twice in the second period to go up 2-1, but Fisher tied it with his second goal of the night with two minutes left before the intermission. Heatley put Ottawa up 3-2 at 1:33 of the third on the power play and Vermette got the insurance goal midway through the period.