The Ducks went up 2-0 in the best-of-seven Western Conference series, which shifts to Minnesota for games Sunday and Tuesday.
Beauchemin scored in the first and second periods while Ryan Getzlaf added a short-handed goal later in the second. Then Anaheim held on after Mikko Koivu pulled the Wild to within 3-2 with 4:56 remaining.
Marian Gaborik had a second-period goal for Minnesota.
Beauchemin beat Niklas Backstrom with a slapshot on a power play late in the second to put Anaheim up 2-1. Getzlaf made a cross-ice pass to Beauchemin from the top of the right circle, and Beauchemin's shot sailed into the upper right corner of the net.
Getzlaf scored 2:26 later, his first short-handed goal ever in the playoffs.
Koivu scored from the top of the crease, managing to get off the shot as he was falling down and beating Bryzgalov to the glove side.
Backstrom faced 25 shots.
Bryzgalov, starting in place of Jean-Sebastien Giguere again, had 24 saves in the Ducks' 2-1 victory in Game 1 victory on Wednesday night. He also started the final three regular-season games while Giguere remained home to be with his wife and newborn son, who had a medical problem.
The Gigueres were concerned that their son, born April 4, might be blind. But while he has no vision in his right eye, a specialist determined earlier this week that the infant does have vision in his left eye.
Gaborik scored at 3:33 of the second to make it 1-1, converting on a goal-mouth scramble for his first goal of the series.
Beauchemin scored midway in the first, his slapshot from blue-line beating Backstrom between his pads.
Beauchemin took Samuel Pahlsson's pass from the left circle and drove the puck low and hard down the slot past Backstrom, who was screened on the play by the Ducks' Rob Niedermayer.
Notes: The Wild won both games at home against the Ducks during the regular season, with the Ducks winning both meetings in Anaheim. ... Bryzgalov, a 26-year-old Russian, won six consecutive playoff games last year while Giguere was injured. The Ducks lost in five games to Edmonton in the conference finals. ... Beauchemin has scored two goals on two occasions for Anaheim in the playoffs, the first time last April 25 against Calgary. The only other Ducks defenceman with two goals in a playoff game was J.J. Daigneault in 1997.