Troy Brouwer and Andrew Ladd both scored in the first period for the Blackhawks, who have won six of their last nine games. Cristobal Huet made 26 saves in a somewhat shaky outing.
Bobby Ryan netted his 22nd goal of the season and Drew Miller also scored for Anaheim, which concluded its six-game road trip with a is 3-2-1 mark. Jean- Sebastien Giguere allowed three goals on 37 shots in the loss.
"We approach each game like the playoffs now," said Giguere. "It's do-or-die for us -- we need to win."
In overtime, Havlat collected a deflected pass in the Chicago defensive zone and used his tremendous speed through the neutral zone to create a partial breakaway. With Anaheim's Corey Perry draped on his back, Havlat, from the low slot, sent a low wrister that beat Giguere inside the right post and Chicago celebrated the victory.
"I saw the puck lying there on the blue line and I took it to the net and scored," said Havlat. "I knew where I was going, and the defenseman got behind me and I just put it in the net."
The Blackhawks grabbed the lead only 1:03 after the opening faceoff on Brouwer's ninth goal of the season. Following a faceoff inside the right circle, the puck was drawn back for a one-timer by Matt Walker from above the circle. The save was made, but Brouwer's rebound backhander from the lower left side beat Giguere.
At the 11:26 mark of the opening stanza, the hosts moved ahead 2-0 courtesy of nifty tic-tac-toe passing. Chicago broke in on a 3-on-1 rush lead by Havlat, who streaked down the right-wing side and passed to the trailer Dave Bolland in the slot. Bolland quickly returned the puck to Havlat, who then passed into the crease for a redirection goal by Ladd from in front.
The Ducks, though, scored twice within a 2:13 span in the early stages of the second stanza to create a 2-2 score.
First, at 2:14, a miscue by Huet led to an easy tally by Miller. Huet went behind the Chicago net to play a dump-in, but he coughed up the puck and Perry gained control. From along the rear boards, Perry quickly passed into the slot and Miller deposited the disc into the open cage.
Shortly after, another error by Huet again proved costly. Chris Pronger's shot went wide and Huet somehow lost his stick during the play. Andrew Ebbett passed from behind the net near the right post into the low slot, where Ryan was in the right place at the right time and his backhander sailed past a stickless Huet.