Chris Neil scored a power-play goal in the first, and Bobby Butler scored on a penalty shot for Ottawa's third goals in a span of 3:52 late in the second.
Brian Elliott made 27 saves, including a stop on Ben Maxwell's penalty shot in the second.
The Senators, who lost 4-2 in Montreal on Friday, evened their record at 2-2.
Maxwell and Tomas Plekanec scored for the Canadiens (1-2).
Carey Price, who allowed four goals on nine shots in 30 minutes on Wednesday night, stopped 24 shots.
Spezza tied it at 2 when he scored from behind the goal line 15:33 into the second. Sergei Gonchar drew an assist in his Ottawa debut when Spezza's shot from the left corner caught Price by surprise.
Maxwell, who scored a power-play goal 1:54 in, was stopped by Elliott on a penalty shot at 16:02.
Ottawa took the lead at 18:32 when Foligno beat Price on a deke. Butler, who was hauled down by Josh Gorges on a breakaway, also faked and shot past Price to make it 4-2 with 34.1 seconds left in the second.
Spezza, who assisted on the Senators' third goal, and Foligno each added their second goal of the game in the third.