Eriksson struck 90 seconds into the extra period, clinching victory for the visitors after they had led Minnesota twice on Wednesday.
Carl Soderberg had given the Bruins the lead in the sixth minute of the NHL encounter thanks to an assist from Eriksson and the two Swedes combined again in overtime to end the Wild's resistance.
The victory took Boston to 35 points in the Eastern Conference's Atlantic division, eight behind leaders the Tampa Bay Lightning, while the Wild are 11 behind Western Conference Central division-leaders the Chicago Blackhawks.
Kyle Brodziak levelled things for the hosts just 27 seconds after Soderberg's opening goal but the Bruins led at the first break when Patrice Bergeron struck.
After a scoreless second period, Minnesota equalised in the 12th minute of the third through Jason Pominville, before Eriksson's overtime heroics secured victory.
In New Jersey, Kyle Turris notched a brace as the Ottawa Senators trumped the home-town Devils 2-0.
The result extended the Devils' losing streak to five games, while Ottawa won for just the third time in 10 matches.
In the other game, the Dallas Stars defeated the Vancouver Canucks 2-0.