With Chicago ahead 5-0, Niemi was seeking his fifth shutout in 11 starts this season, but Petteri Nokelainen scored the first of his two goals with 3:21 left. He connected again 1:19 later.
Niemi, however, stopped several tough chances before Chicago built its lead. The Ducks also misfired or hit the post on others as they lost their third straight and fell for the fifth time in six games.
"The first 10-15 minutes, Antti made several key stops, high-quality saves that kept us in the game," coach Joel Quenneville said.
Had Niemi held on for the shutout, he would have tied Phoenix's Ilya Bryzgalov -- who has played in 37 games -- for the NHL lead. Niemi has been in 13 games overall, including two stints in relief of No. 1 starter Cristobal Huet.
"I know he's been playing unbelievable," Nokelainen said. "He's a good goalie and a great story. He's like any other big guy these days, they cover so much of the net."
Nokelainen wished he had beaten his Finnish countryman much earlier in the game.
"He stopped me a couple of times in the first," Nokelainen said. "I have to bear down and bury those chances early. When it's a 5-0 game, it really doesn't matter much."
Patrick Kane set up two goals, extending his point streak to eight games. The Blackhawks forward has seven goals and seven assists during the run.
Both teams played for the second consecutive night and for the third time in four days. Neither club was sharp early as both failed to convert several close-in chances in the scoreless first period.
Blackhawks defenseman Brian Campbell faked Giguere to the ice about 6 minutes in, but slid the puck through the crease and wide of an empty net.
"He made a couple of nice saves," Blackhawks defenseman Duncan Keith said. "The play was scrambly, and he made a couple of quick saves with his pads. They go unnoticed, but we noticed on the ice."
About 2 minutes later, Anaheim's Kyle Chipchura hit the right post while Niemi was out of position. Niemi then made a point-blank stop on Nokelainen during a Ducks power play with 9:30 left in the first.
"We had our fair share of chances," Anaheim coach Randy Carlyle said. "We had 2-on-1s, hit the posts and had scoring opportunities. He [Niemi] made some big stops, but we didn't do enough to force him."
Versteeg made it 1-0 at 6:21 of the second, capping a rush that began after Niemi stopped Corey Perry on a 2-on-1 rush with a sliding glove save.
Versteeg slipped behind the defense without the puck and took a pass from John Madden just inside the blue line. Versteeg moved unchecked across the crease and beat Giguere with a high shot.
Brouwer made it 2-0 with 4:15 left in the second. He took Kane's feed from behind the net, skated in, and shoveled in a backhander with Giguere down.
Hossa's first goal, at 1:14 of the third, pushed the lead to three goals. His second, during a power play 2:27 later, made it 4-0.
Toews gave Chicago a five-goal edge with 6:10 left when he tipped in Kane's pass.
Anaheim C Ryan Getzlaf, who entered the game tied with Perry atop the Ducks' scoring list, missed his fourth game because of a leg laceration. RW Teemu Selanne sat out his 15th due to a broken hand. ... Chicago D Niklas Hjalmarsson missed his second game after being struck in the head with a puck while on the bench during a win over New Jersey on Thursday. Jordan Hendry took his place in the lineup.
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