Couture scored twice in San Jose's most recent visit to Columbus, a 6-3 loss on Feb. 21 that snapped San Jose's four-game winning streak in the series.
The Sharks, however, may be able to jump-start their offense against the Blue Jackets, who rank near the bottom of the West in goals allowed (38).
Columbus (3-7-2) looks to wrap up a season-high six-game homestand on a positive note after going 1-3-1 in the first five.
Sergei Bobrovsky lost his third consecutive start in a 3-1 loss to Edmonton on Sunday, allowing two goals on only 13 shots.
R.J. Umberger finally scored his first goal of the season for the Blue Jackets, who registered a season-high 40 shots but went scoreless on seven power-play chances.
"Tonight was definitely our highest-scoring chance game that we created," coach Todd Richards said. "The goalie was the difference in the game."
Umberger had a goal and an assist to key the victory over San Jose last February, but has just three goals in 17 career games in the series.
Columbus had scored nine goals in its previous three games before Sunday, but the power play has struggled most of the season, going 4 for 46 over the past 10 contests.
It may not be any easier against the Sharks, who have improved their penalty killing. After allowing a power-play goal in each of its first three games, San Jose has killed 34 straight short-handed situations.
Offense could also be hard to come by against Antti Niemi, who is 3-1-2 with a 1.58 goals-against average in his last six starts.
He's also won four of five career starts with a 2.64 GAA against the Blue Jackets.