Corey Perry had two goals for the Ducks, who were trying to match the franchise record for consecutive wins. Hiller finished with 40 saves, including 15 in the second period and nine more in the third.
"We didn't play the way we really wanted to play," Perry said. "We haven't played that way in a while. Got a point out of it, got to take the positive out of that game. They took it to us in the second and third."
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The Blackhawks got a much-needed boost in their final home date before the first of two six-game trips this season, this time clearing out for the circus to come to town. Backup goalie Corey Crawford made 24 stops for the reigning Stanley Cup champions, who also snapped a four-game home losing streak.
"That was a huge win for us, getting on this trip in a positive way," coach Joel Quenneville said.
Perry tied it at 2 about 3½ minutes into the third, making a nice move to get past defenseman Niklas Hjalmarsson before letting loose with a perfectly placed shot into the upper left corner for his eighth of the season.
It was Perry's 16th career multigoal game and first since he scored twice at Edmonton on March 26.
The Blackhawks had chances to win it in regulation. Hossa banged one off the left post midway through the third and Hiller made a couple of nice stops on short-handed chances by Hossa and Jonathan Toews in the final minute.
Anaheim killed 22 of 24 penalties during its six-game surge, including 17 straight before the Blackhawks solved their special teams twice.
"You never want to give up opportunities on the power play," said Hiller, who needed stitches to close a cut above his left eye after he was struck by a puck during practice Saturday. "I think they have enough great players out there, they make a difference."
Chicago grabbed the lead during a dominant second period. After a penalty for too many men on the ice, Hossa's one-timer was stopped by Hiller but the rebound went right back to the Blackhawks' forward. He converted a backhander with 9:36 left in the period to make it 2-1.
Hossa stopped a six-game pointless streak and ran his career numbers against the Ducks to 13 goals and five assists in 20 games.
Bobby Ryan nearly tied it again during a Chicago line change late in the second, but his shot clanged off the post.
"We didn't have very much energy tonight, we looked tired," Ducks coach Randy Carlyle said. "We've played an awful lot of hockey, and we didn't look like we had the crispness, but we still found a way to get a point."
Chicago got off to a fast start, taking advantage when Ducks defenseman Toni Lydman was sent off for hooking in the first. Patrick Sharp's shot caromed off the backboard to Kane, who shot it into the open left side of the net for his seventh goal.
The Ducks quickly bounced back, tying it 57 seconds after Kane's goal. Under pressure from Jason Blake, Keith lost the puck in Chicago's end. Perry skated away with it before converting Anaheim's first shot of the game 4:34 into the first.
Anaheim C Todd Marchant was scratched because of an upper-body injury. The 37-year-old Marchant is day to day. ... Ducks D Paul Mara played in his 700th NHL game. ... Defensemen Jordan Hendry and John Scott were healthy scratches for the Blackhawks. ... D Sheldon Brookbank and RW Troy Bodie also were scratched for Anaheim. ... The Ducks won seven straight games from Feb. 20 to March 7 in 1999. ... Hossa had three goals in three games against Anaheim last season, but the Blackhawks went 1-3-0 in the season series.