Duncan Keith's first goal of the season, on a first-period powerplay, gave Chicago the lead but they were pegged back by Johan Franzen's third-period equaliser before Nick Leddy won it in overtime.
The St Louis Blues remain the Blackhawks' nearest challengers in the Central Division after also winning in overtime, 5-4 against the Minnesota Wild.
They trailed 3-1 at one point in the second period, Zach Parise scoring twice, but came back to lead 4-3. Dany Heatley forced overtime but Vladimir Sobotka, the eighth goalscorer of the game, won it for the Blues.
Like the Blackhawks, the San Jose Sharks still have a perfect record after their fifth successive win. Joe Pavelski scored twice in a 4-1 win over the Vancouver Canucks.
The Tampa Bay Lightning and Winnipeg Jets each continued their strong starts in the South-East Division.
Tampa's fourth win in five games came against the Philadelphia Flyers, the Lightning recovering from a 1-0 deficit inside the first minute to win 5-1.
Winnipeg had to work much harder before beating the New York Islanders 5-4 in overtime, recovering from 4-2 down with 10 minutes left. Dustin Byfuglien and Alexander Burmistrov forced the extra period and Evander Kane netted the winner.
The Pittsburgh Penguins closed the gap on Atlantic Division leaders the New Jersey Devils with a shootout win over the Ottawa Senators while the Devils went down in overtime to the Montreal Canadiens.
Montreal led 2-0 and 3-1 and, after David Clarkson and Dainius Zubrus took the game to overtime, Andrei Markov scored the Canadiens' winner for the third game in succession.
In Ottawa, goals from Pittsburgh's James Neal and the Senators' Colin Greening cancelled each other out before Neal, Sidney Crosby and Evgeni Malkin settled a high-scoring shootout in the visitors' favour.
Adam Oates collected his first win as an NHL coach as the Washington Capitals beat the Buffalo Sabres 3-2. Alex Ovechkin's game-clinching goal was his first of the season.