The Oilers, headed for the worst record in the NHL this season, lost their 11th in a row.
Minnesota preserved its slim playoff hopes, moving within eight points of eighth-place Chicago in the Western Conference with five games remaining.
Antti Miettinen and Marek Zidlicky both scored on the power play in the opening period, and Brad Staubitz and Havlat tallied in the second.
Tom Gilbert put a slap shot past Niklas Backstrom with 41 seconds to go in the middle period to break up a shutout bid and Linus Omark added a power-play tally for the Oilers with 5:16 to go in the third.
Backstrom stopped 33 shots in Minnesota's second straight win following a season-crushing eight-game losing streak.
Nikolai Khabibulin gave up four goals on 22 shots.