Tuukka Rask made 32 saves and Dennis Seidenberg also scored for the Bruins, who acquired three-time All-Star defenseman Tomas Kaberle from Toronto in one of two trades completed by general manager Peter Chiarelli earlier in the day.
Kaberle made his Bruins debut along with former Senators center Chris Kelly, who was acquired in a trade with Ottawa on Tuesday.
"I got here 20 minutes before warm-up and sometimes it's the best way to do it," Kaberle said. "All the guys were great to me. It was a big win for us and it makes for an emotional day for me after 13 years in Toronto."
Marchand scored his second goal of the game, Boston's third goal of the third period, to put the Bruins up 4-1 at 15:52, just 32 seconds after Seidenberg's power-play goal.
"We're the best team in the third period in the league and we really wanted to use it to our advantage," Marchand said. "We kept building as the game went on and we wanted another big third. These are big points for us and everyone brought it in the third."
Bobby Butler scored for a third straight game early in the second to give the Senators a brief 1-0 lead. Alex Kovalev scored a power-play goal with 1:30 left in the third to draw Ottawa within two.
Robin Lehner stopped 29 shots for Ottawa, which swapped goalies with Colorado on Friday.
"It was a big surprise," Anderson said. "Heading to the rink this morning, going for practice and ready for a little road trip to San Jose, and I got the phone call about two minutes from the rink saying that I've been moved. I didn't see it coming. I was just kind of surprised by it."
Kaberle was acquired from Toronto earlier in the day in a trade that sent Boston prospect Joe Colborne and two draft picks to the Maple Leafs.
"To have a guy like that it gives you extra confidence and obviously ability to make plays because you know that guys are going to have that puck," Bruins captain Zdeno Chara. "He's going to make that play, he's going to make that pass, and to have that it helps everybody, and everybody around is going to be better."
Kelly was traded by Ottawa to Boston on Tuesday night following the Senators' shootout loss to the New York Islanders.
"The first shift was a bit weird but once the game got going I finally felt better," said Kelly, who debuted with Ottawa in 2003-04. "The guys made it easy for me to come in here and play."
The Bruins also traded with Atlanta on Friday, acquiring center Rich Peverley and defenseman Boris Valabik in return for right wing Blake Wheeler and defenseman Mark Stuart. Peverley will join the team Sunday in Boston while Valabik will report to Providence of the AHL.
"I like the direction our management took and we hope to build on that," Bruins coach Claude Julien said.
Marchand scored 6:47 into the second to tie it at 1, using Ottawa defenseman Andre Benoit as a screen to fire a wrist shot past Lehner into the top of the net.
Horton scored his 15th goal 9:47 into the third to make it 2-1. Seidenberg increased the lead to 3-1 with a power-play goal at 15:20.
Anderson arrived at Scotiabank Place after the game was underway. He got dressed after traveling from Denver and took Pascal Leclaire's place as the Senators' backup late in the first period.
"Luckily enough I didn't have to play with jet lag," Anderson said.
Kaberle wore No. 12. The Bruins have retired Hall of Fame center Milt Schmidt's No. 15, which the Czech defenseman wore with Toronto. ... Kelly, who is wearing No. 23 for Boston, raised his stick to acknowledge a standing ovation when a video tribute ran on the scoreboard during a stoppage in play in the first. The No. 22 he wore with Ottawa belongs to RW Shawn Thornton. ... Benoit played his first NHL game. RW Francis Lessard, who was recalled along from Binghamton of the AHL along with Benoit, made his Senators debut. ... Leclaire has missed 25 games in a row because of a lower-body injury. He had not been in uniform since Dec. 17, when he was injured in the warm-up prior to a 6-5 overtime loss in Colorado.