Stalberg redirected Duncan Keith's shot past Jonas Hiller for his sixth goal and second in two nights. Patrick Kane and Marian Hossa each had a power-play goal and an assist to help the Blackhawks snap a three-game slide.
Corey Perry had two goals for the Ducks, who were trying to match the franchise record for consecutive wins.
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 annual circus run. The reigning Stanley Cup champions also snapped a four-game home losing streak.
Perry tied it at 2 about 3 1/2 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. It was his eighth of the season.
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.
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.
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.