The Senators were leading 2-0 with less than 5 minutes to go in regulation but allowed the Hurricanes to come back.
Carolina's Tuomo Ruutu collected a loose puck in front of the net and shoveled it past Ottawa's Craig Anderson, and Jeff Skinner tied it 2 1/3 minutes later when he deflected Jamie McBain's shot from the point into the net.
Spezza and Zenon Konopka notched first-period goals and Anderson finished with 32 saves for the Senators, who earned a third straight win.
Ward turned aside 26-of-28 shots for the Hurricanes.
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