Trevor Daley and Erik Cole also scored in the second, as Dallas turned a 3-1 deficit into a 5-3 lead.
Anders Lindback stopped all 14 Ottawa shots in the period. He made 34 saves and gave up two goals in relief.
Starter Kari Lehtonen allowed two goals in five shots while playing just 10:30 before his earliest exit this season.
Ottawa's Mike Hoffman, Clarke MacArthur and Jared Cowen each scored in the first period. Milan Michalek added a third-period goal.Dallas' Cole and Ales Hemsky each had a goal and an assist.