Jaden Schwartz scored for Seattle (40-25-8), which is 2-2-1 in its past five games. Philipp Grubauer allowed four goals on 13 shots before being replaced by Martin Jones, who made six saves in relief.
The Kraken fell five points behind the Edmonton Oilers for third in the Pacific Division. The Oilers won 5-4 at the Arizona Coyotes on Monday.
"It was one of those nights where we weren't rewarded for some of the good, hard work we did offensively," Seattle coach Dave Hakstol said. "We made too many mistakes that ended up in the back of our net. It felt like we could keep pushing and find one, especially in the first half of the hockey game … and get ourselves right back into it, but that didn't happen."
Middleton gave Minnesota a 1-0 lead at 15:17 of the first period. Jared Spurgeon faked a slap shot from the point before passing to Middleton, who skated into the left circle and beat Grubauer glove side.
"We didn't play that well in the first, so it was nice to get a quick one like that," Middleton said. "I had the easy part of that whole shift. … 'Spurge' making a great pass, [Eriksson Ek] screening."