Palmieri beat Joey Daccord glove side on a forehand-to-backhand move.
It was Rittich’s first shutout of the season and eighth in the NHL, and Daccord’s second this season and seventh of his career.
The Islanders (13-8-2), who were coming off a 2-1 loss to the St. Louis Blues on Saturday, have won seven of nine (7-2-0).
Daccord made 35 saves for the Kraken (11-5-6), who were coming off a 3-2 overtime win at the Pittsburgh Penguins on Saturday, and had won four of their past five.
Rittich got his right pad down at 11:17 of the first period to deny a Matty Beniers breakaway try.
Daccord slid out to the top of the crease to deny an Anders Lee point-blank try at 17:19 of after Mathew Barzal found him alone in the slot.
Daccord slid over to deny Barzal at the glove-side post off a feed from Horvat at 13:20 of the second period.
Through two periods, the Islanders doubled up Seattle in shots, 20-10.
Rittich got his right shoulder on a Jaden Schwartz wrist shot at 18:21 of the third period.
The Islanders outshot the Kraken 3-1 in overtime.