Pierre-Luc Dubois had a goal and an assist for the Blue Jackets, which ended a three-game losing streak (0-2-1).
"I thought we played one of or more complete games, albeit I think against a tired team, but it's a team that works hard," Columbus coach John Tortorella said. "It's an important win for us, obviously."
Thatcher Demko made 28 saves for Vancouver (32-34-10), which is seven points behind the Colorado Avalanche for the second wild card in the Western Conference with six games remaining. Vancouver lost at home for the second straight night after being defeated 3-1 by the Calgary Flames on Saturday.
"It was a desperate team we played," Demko said. "I don't think they let up at all. They played a pretty structured game, a pretty solid game throughout."
Anderson made it 1-0 with a wrist shot from the right face-off circle at 16:19 of the first period for his 25th goal of the season.
"We knew the first goal was going to be really important," Anderson said. "After we got that first one, we had a little more jump in our game. We didn't have any passengers tonight. Everyone was on board."