Philipp Grubauer made 21 saves for the Kraken (15-5-3), who won their fourth straight overtime decision after coming back from down 2-0 after the first period.
"That was a hard-fought game, it's two good teams, right down to the wire," Hakstol said. "We did a lot of little things that guys in this room did during that hockey game in order to stay with it and not just find one point but get the extra point."
Alex Ovechkin had two assists for his 120th multiassist game, and Darcy Kuemper made 22 saves for the Capitals (10-11-4), who are 1-1-1 thus far on a six-game road swing.
"Not enough of the good stuff tonight, not enough of the right things," Washington coach Peter Laviolette said. "Everywhere, everywhere, the whole night, all three periods. There's nothing I'm happy about tonight."
Yanni Gourde tied it 2-2 at 17:33 of the third period when he backhanded in a rebound from a Daniel Sprong shot from the left side of the net.
"We've been doing a good job of finding ways to win and staying with it and a lot of momentum swings and games and we're doing a pretty good job of managing that," Kraken forward Jaden Schwartz said. "Whether it's special teams power play getting a big goal, or the penalty kill stepping up and it's a big save by [Grubauer]. Everyone's chipping in and playing together and we're getting results."