The Wild had won their previous two games and took the lead midway through the first period when Marco Scandella scored his first of the season on a wrist shot.
Minnesota was shut out the rest of the way by Viktor Fasth, who made the second start of his NHL career.
Palmieri tallied 6:49 into the second period and then delivered the tying goal 4:21 into the third on a slap shot. Bobby Ryan scored on the power play with 1:34 remaining to give the Ducks some insurance.
Fasth made 26 saves and has won both his starts with Anaheim. Niklas Backstrom stopped 28-of-31 shots for Minnesota.