ST. LOUIS -- Before each home game, the St. Louis Blues play the Bon Jovi anthem "This is Our House." They might want to play something different the next time the San Jose Sharks come to town.

The Sharks have played as of Scottrade Center is their home rink of late, and they did it again on Monday night.

Left winger Tomas Hertl and centers Logan Couture and Joe Thornton each scored two goals to carry the Sharks to a 6-3 win over the Blues.

The win was the fourth for the Sharks in their past five games in St. Louis. San Jose is 9-3-0 in its past 12 road games overall.

Thornton also had two assists on the night, giving him his first four-point game since Oct. 15, 2013 -- in St. Louis.

Couture's second goal turned out to be the most important of the night for the Sharks, as it gave them a 4-2 edge seconds after a St. Louis goal.

San Jose built a quick 3-0 lead in the first period thanks in part to two power-play goals after Blues right winger Ryan Reaves received a major penalty for boarding and a game misconduct.

Reaves' hit knocked Sharks defenseman Matt Tennyson out of the game, and there was no information available after the game about the extent of Tennyson's injury.

The Sharks already led 1-0 before scoring during the major penalty and adding a second goal during a five-on-three advantage after a slashing penalty on defenseman Robert Bortuzzo.

"I think we came out ready to play and were carrying the play," Sharks coach Peter DeBoer said. "That's the ultimate retribution for a hit like that, to score two or three power-play goals. That decision basically cost them the game."

The Blues rallied to close the gap to 3-2 on power-play goals from center David Backes -- the 200th goal of his career -- and right winger Vladimir Tarasenko.

Tarasenko's team-high 29th of the season came 11:25 into the second period.

The momentum lasted for just 20 seconds however, before Couture's goal restored the two-goal lead and sent the Sharks to their fifth win in their past seven games (5-1-1).

"When we made it 3-2, I thought if we could have built some good shifts off of that, we could have been in good shape, but to get scored on right away took all the air out of the balloon for us," Blues coach Ken Hitchcock said.

Couture noticed that shift in momentum as well.

"To get it back to 4-2 was huge for us," said Couture, who had the 19th two-goal game of his career. He has never completed a hat trick.

"It would be nice to have one," he said. "I didn't really have much in the third. We were trying to lock it down defensively, and I thought we did a pretty good job of that. It's nice when you get a couple bounces and the puck finds its way in the net for you."

The loss snapped a five-game winning streak for the Blues, who had not lost in regulation in seven games (6-0-1) since a 3-1 defeat to the Sharks on Feb. 4 in St. Louis.

The Blues, who have had to deal with several significant injuries throughout the season, also saw goalie Brian Elliott leave the game following the Sharks' third goal in the opening period.

Elliott sustained what was announced as a lower-body injury, and he will be re-evaluated Tuesday.

Jake Allen replaced Elliott in goal, his first game since he was injured Jan. 8. He was activated from injured reserve Sunday and was not expected to play until this weekend.

"I hadn't played in a month and a half," said Allen, who stopped 15 of the 17 shots he faced. "I got my feet wet. We started slow. We were too far behind the eight ball to catch up at the end. For me personally, it was sort of nice to get some game action and game speed."

Both of Thornton's goals came in the third period, including an empty-net tally with 1:25 to play.

NOTES: LW Magnus Paajarvi, a healthy scratch for the past five games, replaced LW Alexander Steen in the Blues' lineup. Steen will miss at least four weeks with an upper-body injury he sustained Saturday night at Arizona. ... The Sharks said they hope C Nick Spaling and D Roman Polak, acquired Monday from Toronto, will join the team before Wednesday night's game in Colorado. ... The Sharks also expect D Brendon Dillon, who missed his sixth consecutive game Monday night, to return Wednesday. ... The Blues host the New York Rangers on Thursday night before beginning a four-game trip.