"They played hard and desperate and we sat back a bit," Chuck Kobasew said. "It was big to get a win and we had to find a way to get it done."
Boston had won nine straight before dropping two in a row.
"This was really important and to get over the hump was the toughest thing," Boston goalie Manny Fernandez said. "If it's going to be like this for a while, we have to work twice as hard at limiting our mistakes."
Ottawa lost for the seventh time in its last eight games.
Krejci put the Bruins ahead 4-3 when he stole the puck from Daniel Alfredsson at the side of the net and backhanded a shot toward goalie Martin Gerber. Gerber blocked it back to Krejci, who knocked in the rebound at 10:13 of the third period.
"You try to trust your best guys," Senators coach Craig Hartsburg said. "It's those guys that cost us the game."
Savard gave Boston a two-goal advantage with 5:31 remaining, and P.J. Axelsson scored an empty-net goal with 41 seconds left. Savard also had two assists and leads the Bruins with 52 points.
Boston avoided losing three straight for the second time this season.
"I guess the win itself was important, although the way we won it wasn't so good," Bruins coach Claude Julien said.
After struggling through an unusual two-game losing streak, Boston took a 2-0 lead 4:15 into the first period. Aaron Ward's slap shot beat Gerber at 2:20, and Kobasew drove to the net and knocked in Dennis Wideman's shot for a two-goal lead.
"We had an unbelievable start and that's what we wanted," Bruins forward Blake Wheeler said.
Chris Phillips cut Boston's lead in half when his wrist shot squeezed through a screened Fernandez at 12:14 of the first period.
The teams traded goals midway through the second period. Michael Ryder made it 3-1 when he jammed home the rebound of Blake Wheeler's shot at 8:44, and Chris Kelly narrowed cut it to 3-2 after taking advantage of Wideman's turnover.
Gerber allowed five goals on 22 shots for Ottawa, 1-13-3 in its last 17 road games. The Senators' lone win came on Dec. 30 in Edmonton.
While responding to questions about Hartsburg and general manager Bryan Murray possibly being under fire, Gerber said "We didn't do anybody any favors tonight. ... We want to get out of this whole mess."
Ottawa's Antoine Vermette scored his fourth goal of the season with 28 seconds remaining.
Ottawa's Jarkko Ruutu served the first game of a two-game suspension for biting Buffalo's Andrew Peters. ... Marc Savard played in his 700th game. ... Jason Spezza's first-period assist extended his point streak to five games. ... Boston beat Ottawa for the fourth consecutive time. ... Milan Lucic missed the game because of an undisclosed injury.