Artemi Panarin scored the game-winner and Toews had a pair of goals in the third period when the Blackhawks (47-20-5) tallied four times in three minutes to erase a two-goal deficit. With Chicago trailing 3-1, Toews redirected a Duncan Keith shot and pushed it past Avalanche goalie Jeremy Smith, who hadn't allowed a goal since the first period.
Smith finished with 28 saves for Colorado (20-48-3), which gave up at least four third-period goals for the second straight night.
Avalanche coach Jared Bednar challenged the goal after it appeared Toews was offsides as the Blackhawks entered the offensive zone. But after a video review, officials determined the goal stood as officials in the NHL situation room in Toronto determined it was inconclusive as to whether Richard Panik touched the puck before Toews crossed the blue line while attempting to avoid being offsides.
Panik scored 17 seconds after Toews' controversial goal to tie the game at 3 before Panarin gave Chicago a 4-3 lead just 17 seconds later. Toews continued the scoring barrage with his second goal of the period to break the game open.
Marcus Kruger tallied an empty-net goal to close out the victory, which was Chicago's 17th in its last 20 games.
Colorado led 3-1 after two periods.
With the Avalanche clinging to a one-goal lead, Sven Andrighetto widened the gap with less than four minutes remaining in the second period when he redirected a Mark Barberio shot past Scott Darling to provide some breathing room.
Moments earlier, Darling made a sprawling save to keep the Avalanche from extending their lead. Mikko Rantanen appeared to have an angle on an empty net and flipped a backhanded shot on goal from point blank range, but Darling made a skate save to keep the Blackhawks within a goal.
Mikhail Grigorenko, who hadn't tallied a goal since Feb. 25, provided the Avalanche with a 2-1 lead with just under five minutes to play in the first period. Grigorenko rattled a shot past Darling for his second goal of the night as Colorado erased an early deficit.
His first goal came directly in front of Darling when Grigorenko found the puck on his stick after the Blackhawks failed to clear the puck out of the Avalanche zone.
Patrick Kane gave Chicago a 1-0 lead with his 32nd goal of the season. Kane, who has scored 17 goals in his last 20 games, took a pass from Panarin and fired a shot past an outstretched Smith 4:33 into the game.
NOTES: Avalanche G Jeremy Smith made his first start since March 5 after Calvin Pickard allowed five goals Saturday against Detroit. Coach Jared Bednar said he planned to give each a start in the back-to-back games and went with Pickard on Saturday after a strong start against the Red Wings on March 15. ... C Mikhail Grigorenko replaced John Mitchell on Colorado's third line. ... D Cody Goloufbef and D Patrick Wiercioch were also scratched. ... Blackhawks RW Marian Hossa missed his second straight game with a lower-body injury. Coach Joel Quenneville said before Sunday's game Hossa would likely play. ... Scott Darling made the start, his second since March 1, on Sunday in net after Corey Crawford had appeared in four of Chicago's five last games. ... D Johnny Oduya (rest) did not play with the Blackhawks playing for the second time in two nights. .... C Dennis Rasmussen and D Michal Rozsival were scratched.