Alex DeBrincat, Jonathan Toews and Brent Seabrook also scored, and Cam Ward stopped 22 shots. Maxime Lajoie scored for Ottawa in his NHL debut, Colin White and Zack Smith added goals, and Craig Anderson made 37 saves.
Seabrook tied it midway through the third period, with Kane find the defenseman alone in front for a one-timer.
The teams combined for five goals in the first period.
Chicago opened the scoring when DeBrincat used Thomas Chabot as a screen before firing a shot past Anderson. Ottawa tied it when Smith's shot deflected off Duncan Keith. The goal was Smith's first since Feb. 21, also against Chicago.
The Hawks regained the lead when Toews came down the wing and fired a shot off Anderson's shoulder.
The Senators tied it in Lajoie's one-timer, and White made it 3-2 on a power play.