Bergeron scored the game-winner in the second period as Edmonton moved to within three points of second-place Minnesota, which trails first-place Vancouver by just two points.
"Now we are three points back, that's a big difference," said Edmonton's Shawn Horcoff. "There is a lot of hockey left to be played and you can't get caught too far behind. It is just too hard to make up points in February and March."
Edmonton took a 1-0 lead on Lupul's 13th goal of the season with 2:29 remaining in the first period. The power-play tally came with Brent Burns in the penalty box for tripping.
Bergeron scored on the power play in he second to give the Oilers a 2-0 lead.
Wes Walz scored for the Wild in the third to spoil Dwayne Roloson's bid for a shutout.
Roloson made 28 saves while Manny Fernandez faced just 18 shots for the Wild.