Horton scored two goals and the Bruins beat the Lightning 4-2 on Thursday night.
"He's one of the elite right wingers in the league when he's on top of his game," Boston coach Claude Julien said. "He's got so much potential, and we know that. He's been through some tough times with that concussion, and hopefully we get him back healthy and get some consistency out of his game because he certainly deserves it."
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After blowing a two-goal lead, the Bruins took a 3-2 advantage on Marchand's goal from the slot with 6:02 to go in the second. Horton extended the lead to 4-2 when he redirected Zdeno Chara's pass at 2:33 of the third.
"We wanted to make sure that we got the first one tonight and try to quiet the crowd down a bit," Marchand said. "Luckily, we got two. We kind of saved ourselves a little bit of trouble after they came back."
Marchand has nine goals on 20 shots this season.
"That's what we've got to aim for, beat that kind of team," Lightning coach Guy Boucher said. "At ice level, this was probably the most intense game of the year."
The Lightning went 0 for 3 on the power play. Boston has given up just three goals in 54 short-handed situations.
"They don't give up much on the PK," Stamkos said. "So that's definitely an area we could have been a lot better. We couldn't even get into the zone."
The Bruins took a 2-0 lead early in the first on goals by Horton and Bergeron.
Horton scored on the rebound from the low left circle 1:11 into the game. Bergeron made it 2-0 when he beat goalie Anders Lindback from the right circle at 3:50.
"We had a good start," Horton said. I think that's what carried it through the game."
Tampa Bay got within 2-1 on Stamkos' 11th goal of the season with 11:47 left in the first. Teddy Purcell set up the goal after winning a battle for the puck in the slot.
Purcell finished with two assists.
Conacher got a wrist shot from the left circle past Tuukka Rask 9 minutes into the second that tied it 2-2. The rookie snapped an eight-game drought with his sixth goal of the season.
"It seems like when we don't have that home-crowd pressure on us we can play our game, and it's been working pretty good this year," Rask said.
- Boston D Dougie Hamilton had two assists.
- Stamkos has four goals in three games.
- Boston LW Milan Lucic was back in the lineup after he missed Sunday's 3-2 win at Winnipeg because of a personal matter.
- Tampa Bay D Keith Aulie didn't play due to flu-like symptoms.