Ottawa was outshot 37-20 but scored three unassisted goals after takeaways, one on the power play and another short-handed, by Pageau.
Craig Anderson made 33 saves in his third straight win, including two shutouts.
Pageau scored on two breakaways, including his league-leading third short-handed, and added an assist. He has six goals this season.
Dallas goalies Antti Niemi and Kari Lehtonen combined to make only 13 saves.
The Senators' Mike Hoffman also had two goals, one into an empty net. Mark Stone had a goal and two assists. Bobby Ryan and Milan Michalek also had goals.
NHL leader Jamie Benn scored his 15th and 16th goals for Dallas. Benn assisted on Tyler Seguin's goal. Patrick Sharp also scored for the Stars.