Zibanejad scored a power-play goal and had an assist on Alexis Lafreniere's goal to give him points in three straight games (two goals, three assists) and in 15 of 18 (12 goals, 14 assists) since Dec. 15.
The Rangers (29-13-4), who had lost two in a row, were outshot 42-24.
"I think it was awful," Rangers coach Gerard Gallant said. "Love the win. Competitiveness, quite a bit, disappointing.
"They play hard, they send four lines at you and I'm not disrespecting their team. I'm talking about my team and we just weren't hard enough."
Jared McCann scored his team-leading 18th goal for the Kraken (14-26-4) and Philipp Grubauer made 21 saves, including stopping Miller on a breakaway at 13:45 of the third period.
"There's not much you can say about it, that wasn't a breakdown or anything like that, it was just a face-off win with a pick and they scored," Seattle captain Mark Giordano said of Miller's goal. "We played pretty hard and I thought fought right to the end. It [stinks] the way we lost, there's no other way to put it."
Shesterkin stopped all 14 shots he faced in the first period, 10 of 11 in the second and 16 of 17 in the third.
"Excellent," Gallant said. "He gave us a chance to win and that's what he does."
Seattle coach Dave Hakstol said he didn't want to dissect what happened on Miller's game-winning goal because it would take away from his team's strong performance.
The plus-18 shot differential is the Kraken's widest this season.
"When we take care of the puck and manage it well and make sure we're not giving away anything easily, especially off of the rush, we become difficult to play against," Hakstol said. "That's the way we played."