New York jumped out to a 2-0 lead in the second period on scores by Boyle and Stepan. Boyle slapped the puck past Elliott at 10:36 for the first goal. Stepan scored short-handed, knocking in the rebound of a shot by Ruslan Fedotenko at 15:55.
Spezza pulled the Senators to 2-1 when he snuck the puck past Lundqvist with 24 seconds left in the second period.
Ottawa then tied it on Karlsson's gloveside goal 40 seconds into the third. Spezza's second goal of the game and fourth of the preseason gave the Senators a 3-2 lead at 5:32.
Boogard, known for his physical presence on the ice, tied it about a minute later after a nice pass from Brandon Prust. Boogard had gone 222 straight regular season games without scoring a goal.
The Senators briefly led again after a goal from Campoli made it 4-3 but Staal tied it with 3:59 left in regulation.
The teams wrap up their preseason schedules tomorrow night at Ottawa in the second game of the home-and-home series.