Vince Dunn had three assists, Victor Rask had a goal and an assist, and Chris Driedger made 12 saves for the Kraken (25-44-6).
"We skated and we had pretty good pressure everywhere," Hakstol said. "It almost seemed like we were a step quicker than they were most of the night, and that's when playing without the puck, That's important, and with the puck even more important. We made a couple of mistakes in the second period, and they took advantage of it. We made a couple of mistakes with the puck and that leads to pretty good opportunities for them."
Brady Tkachuk scored his 28th goal, and Anton Forsberg made 25 saves for the Senators (28-41-7), who were held to a season-low 14 shots.
"I just didn't think we played our game long enough," Ottawa defenseman Nick Holden said. "We had a few stretches where we played real fast, playing behind them, and scored some goals and had some success doing that, but I felt like we were turning too many pucks over and playing a little slow."
Daniel Sprong gave the Kraken a 1-0 lead at 4:36 of the first period on a one-timer from the left circle on a power-play after Rask found him with a cross-ice pass.
Sprong has four goals in 11 games since he was acquired in a trade with the Washington Capitals on March 21.
"Rask made a great play," Sprong said. "I've watched the greatest goal scorer [Alex Ovechkin] of all time for two years in that spot. I learned a lot from him over that time, which I'm very grateful for. He was really good to me, talking to me about things like that. I just know I've got to find that area, and then I know I've got to get that shot."