Brandon Hagel scored two goals, and Jonathan Toews had three assists for the Blackhawks (1-7-2), who set their record for most consecutive games without a win to begin a season (nine) in a 1-0 loss at the St. Louis Blues on Saturday.
Kane returned after missing four games while in NHL COVID-19 protocol.
"Feeling good," Kane said. "Had a bit of symptoms to start my time out, but after a couple of days, I felt pretty good. Because I had symptoms and the rules and protocol, I had to be out 10 days. That was the situation, but (I) felt good for the most part through all of it.
"There's obviously been a lot going on, and even though I wasn't with the team the past 10 days, you could feel not having a win weighing on us. It's just huge to get the first one. Now we kind of got the monkey off our back."
Alex Formenton scored, and Matt Murray made 26 saves for the Senators (3-5-0), who were 0-for-4 on the power play and lost for the fourth time in five games.
"Too many passengers," Ottawa coach D.J. Smith said. "We didn't have good legs, for whatever reason. We weren't sharp, and you could just see it from our first power play. We had great looks and just didn't make the plays. Then they scored and we got a little frustrated. We worked uphill all night. Give them credit. Kane came to play tonight, and he took us apart."
Marc-Andre Fleury made 29 saves for Chicago, including 13 in the first period.
"It's more a big gorilla (off our backs), not just a small monkey," Fleury said. "Definitely feels good. It's been rough, it's been tough. Guys stuck with it, kept practicing hard, kept trying hard and tonight things went well. The PK was good, power play was good, we had a great second and third period. Fun to give the fans something to cheer about."
Hagel gave the Blackhawks a 1-0 lead at 19:10 of the first period on a rebound of Kane's shot.