The Leafs snapped a four-game losing streak with the victory, and extended the Blackhawks' record to 0-6-1.
John Tavares and David Kampf also scored for Toronto, and Jack Campbell stopped 25 shots.
''This feels good, getting two points at the end of a long road trip,'' Toronto coach Sheldon Keefe said.
Chicago got 36 saves from Kevin Lankinen, and goals from Kirby Dach and Alex DeBrincat.
The decisive OT goal happened when Nylander broke in on a 2-on-0 and snapped a wrist shot past Lankinen.
''It hasn't been looking too pretty the last few nights,'' Nylander said. ''Tonight, we got closer to where we want to be, but not fully there yet. I just tried five-hole and it worked.''
The Maple Leafs outplayed Chicago as the game went on, but the Blackhawks ended one streak early, taking the lead for the first time this season when Dach beat Campbell with a power-play wrist shot over the glove side 5:44 in.
The Blackhawks had been tied or trailed for more than six games at that point, the longest such streak in the NHL since 1979-80.
DeBrincat scored at even strength for a 2-0 Chicago lead at 11:48 of the first, accepting Seth Jones' long pass following Toronto defenseman Justin Holl's turnover. DeBrincat's shot sailed over Campbell's shoulder.
''We played more the style we want to play,'' Chicago's Tyler Johnson said. ''There were still moments we played too cute, not making the simple plays.''
Keefe said the Leafs ''talked a ton about protecting our goal and they scored two. That's got to stop.''
Tavares cut the lead to 2-1 at 6:14 in the second, outmuscling Jonathan Toews in the slot and backhanding a shot over Lankinen's glove hand.
''A good character win,'' Tavares said. ''We had a good (first) intermission, getting our mindset right. We challenged each other.''
Kampf, a former Blackhawk whom the Leafs signed as a free agent in July, tied the game at 2, beating Lankinen on a sneaky backhand from the slot with 7:29 left in regulation. Kampf took a pass from Rasmus Sandin on the boards and barely looked at Lankinen as he let the shot go.
NOTES: Chicago's Patrick Kane, Henrik Borgstrom, Jujhar Khaira and Riley Stillman remain in COVID-19 protocol and missed the game. Toews tested negative earlier on Wednesday and was put back on the active roster. . The non-sellout crowd in the United Center was noticeably subdued in the day after revelations that team executives in 2010 failed to take allegations of sexual assault by then-assistant coach Brad Aldrich against a backup player to authorities. The player, Kyle Beach, came forward in a Canadian television interview on Wednesday. ''At the end of the day, my heart goes out to Kyle,'' Blackhawks captain Toews said. ''It's not an excuse looking back, but the truth is, a lot of us were focused on hockey every single day. You hear rumors, but it's at the back of your mind.''
Chicago: Hits the road for two games against teams that are 5-0-0, at Carolina on Friday and at St. Louis on Saturday.
Toronto: Begin a five-game homestead on Saturday, hosting Detroit.
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