Schwartz was a big reason why Seattle was better. He put the Kraken ahead 3-2 at 18:59 of the second period when he found open space between the hash marks and scored off a pass from Eberle.
Schwartz then made it 4-2 at 1:03 of the third period with a shot from the right face-off dot.
The goals were the forward's first points in four games since he returned from an undisclosed injury that caused him to miss eight games.
"Not playing a game for maybe three, four weeks, just felt a little bit off, legs and timing a little bit," Schwartz said. "I think any player would tell you when you miss some time, it's a little bit of an adjustment. ... I've had some practices and a few games under my belt.
"When you're out you can kind of do as much as you can in the gym and on the ice, but nothing feels the same as it does when you're actually in a game. I'd say tonight my jump felt a lot better than in the first couple games."
Seattle coach Dave Hakstol said Schwartz's presence, as much as his goal scoring, helps the Kraken.
"The one that you don't see is his presence in the locker room," he said. "He's the guy that keeps a lot of guys around him loose. He's won and he's got that presence, and he's pretty timely in the way he delivers some of his leadership.
"On the ice, a lot of it is about possession. He's a guy that is not a big guy, but he is great on the walls, he creates possession down low, and it was nice to see him finish on two for us, and those were big."