Korpisalo was bidding for his second straight shutout against Washington. He won 3-0 Dec. 16.
"He was unbelievable. He made some saves that, I mean, I think we were a little rusty and thank God he wasn't," Blue Jackets forward Nick Foligno said. "I think he was in the goalie simulator all break. He's been that [good] for us the last little bit here, which is huge and a big reason why we've had success."
The Capitals were 1-for-5 on the power play after going 0-for-15 their past five games. Columbus was 0-for-2.
Lilja, playing his 13th NHL game, made it 1-0 at 9:17 of the second period. Riley Nash took a pass from Ryan MacInnis in the left circle, eluded a sliding Jonas Siegenthaler, and passed across the slot to Lilja for the one-timer.
Hagelin tied the score 1-1 when he knocked in his own rebound at 6:13 of the third period after a feed across the slot from Richard Panik. It was Hagelin's first goal of the season.
"It was a great pass. I think he's been on my side the whole time," Hagelin said of Panik. "He's been trying to find me out there and I've just missed some good looks, but today it went in."