Pittsburgh won its sixth in a row, tying idle Anaheim for the longest current winning streak in the NHL.
Kunitz put a slap shot past Niklas Backstrom with 9:17 to go in the second period, giving the Penguins a 4-0 lead. It was the 19th tally of the season for Kunitz, moving him into the top five among NHL goal scorers this season and bringing him within seven of equaling his career-best campaign of two years ago.
The Wild cut their deficit to 4-2 before Olli Maatta scored shorthanded for the Penguins 7:54 into the third.
Jeff Zatkoff improved his record to 6-2-0 by making 24 saves. Backstrom allowed all five Pittsburgh goals on 36 shots.