After Chicago blew a two-goal lead in the final 2:01 of regulation, Daze broke out with Steve Sullivan on the odd-man rush and fired a slap shot from the right faceoff circle over goaltender Patrick Lalime's shoulder.
It was Daze's second-game winner and gave the Blackhawks their seventh victory in eight games.
Chicago, which struggled through an eight-game road winless streak last month, recorded its sixth win in the last seven away from home and improved to 9-9-4 on the road.
Daze got his first goal four minutes into the third period to break a 1-1 tie, then tipped Michael Nylander's wrist shot between Lalime's pads at 16:25 to give Chicago a 4-2 cushion.
Peter White and Sullivan scored the other goals for the Blackhawks and Jocelyn Thibault made 29 saves for his third straight win.
Chris Neil and Daniel Alfredsson each scored twice for the Senators, who have one win in their last four home games.