John Hayden, Dylan Strome, Patrick Kane, Drake Caggiula and Dominik Kahun had goals in the third. Four of the five were scored in 2:48.
"It is nice to keep this roll going and finally turn things a bit," Blackhawks coach Jeremy Colliton said. "We have a bit of momentum and we are playing well. When you have the momentum and keep playing well, you usually get the results. We just need to keep pushing and we will get our points."
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Kane, who also had an assist, extended his point streak to 12 games. He has 10 goals and 18 assists over that stretch.
Erik Gustafsson scored in the first period for Chicago (21-24-9), and Cam Ward made 25 saves. Jonathan Toews and Brandon Saad each had two assists.
"We know what we are doing is working and we are hanging in games," Toews said. "Whether we are ahead or down a goal going into the third period, we can find ways to create offense and come out on top. We had offense from all over our lineup tonight, which was great. It is nice for our team to win in different ways. It only adds to our confidence."
Leon Draisaitl scored two goals and Connor McDavid had two assists for Edmonton (23-25-5), which has lost six in a row (0-4-2). Cam Talbot allowed four goals on 27 shots before being pulled at 5:51 of the third period. Mikko Koskinen made six saves.
"Same type of thing as the last couple of games; we control a lot of the first two [periods], and then go to sleep in the third," McDavid said. "I'm not sure what that is."