Zubov and Jokinen scored on their shootout attempts before Minnesota's Brian Rolston answered.
Ribeiro clinched the victory when he faked to his right, and took a shot to his left that beat Wild goalie Niklas Backstrom.
Dallas, 2-0 in shootouts this season, improved to 14-1 in the tiebreaker the past two seasons.
Rolston, Mikko Koivu and Petteri Nummelin had goals for the Wild, who have lost four in a row.
Jokinen's seventh goal of the season tied it with 4:17 left. Philippe Boucher and Loui Eriksson added goals for Dallas.
Minnesota has won just four times in 16 games.