DENVER (AP) -- For 59 minutes, the Colorado Avalanche were on their way to a bad loss. The final 58 seconds of regulation changed that.
"This was big because we needed these points," Blake said. "I got a power play at the end and Danny made a strong move down the wall, put the puck to the net and it went in."
Calgary lost one point off its division lead by falling in a shootout to Detroit at home Monday. Both the Flames and Avalanche have seven games remaining. Colorado will play its final three games on the road.
"It was a tremendous sense of relief to see the last goal go in," Colorado coach Joel Quenneviile said. "We were thinking before if we could get it to overtime, then we get a free point and then we got a really lucky break after that."
"We made a generous gift to them," goalie Nikolai Khabibulin said. "They really needed one and we gave it to them."
Brown gave Chicago a 3-2 lead with 5:21 left in the third when he took a centering pass from Bourque from behind the net and sent a backhander over goaltender Peter Budaj's glove.
But with 2:03 remaining, Michal Barinka was sent off for cross-checking. Blake tied it 3-3 at 19:03, sending the puck through a pileup in front of the net and past Khabibulin.
Hinote scored from a tough angle after Sakic had dumped the puck into Chicago's zone. Hinote skated along the right boards and sent a shot off the back of Khabibulin's right pad and into the net with 12 seconds left.
"I only get the lucky ones," Hinote said. "I knew there was about 15 seconds left so I just wanted to throw it to the net and maybe get a faceoff down there. I wasn't trying to score from there."
"He's right," Khabibulin said of Hinote's goal. "That puck shouldn't go in. I'll take the blame for that one."
Chicago outshot Colorado 9-6 in the first period and showed some grit after Khabibulin gave up a rebound goal to Blake at 5:09. Sakic's wrist shot was stopped but the puck bounced right to Blake, who tapped it in for his first of the night.
Sharp took a pass from Mikael Holmqvist and ripped a slap shot from the upper right circle at 7:13 of the period for his 12th of the season.
Bourque gave Chicago a 2-1 lead when he scored between Budaj's pads at 8:13. Brunette tied it with a power-play goal at 13:34.
"It's tough to play teams like this," Blake said. "They are playing for their jobs and they come after you."
Brown countered, "We have been through a lot this year. The effort was there, but unfortunately, something weird happened, and we don't get anything out of a good performance."
The teams went 2-2 in the four-game season series. ... The Blackhawks are 11-25 in one-goal games.