Boston took an early 2-0 lead, but failed to score during the final 50 minutes and had a four-game winning streak halted.
Chris Neil scored for the Senators with 50 seconds to go in the first period to cut Ottawa's deficit in half and Spezza tied it 1:32 into the second.
Spezza then assisted on a goal by Jared Cowen, which came on a slap shot with 14:18 left in regulation. Bobby Ryan added an insurance goal midway through the third.
The Boston goals came from Loui Eriksson and Brad Marchand.
Notable deaths of 2014 [PHOTOS]