Spezza, back in the lineup after missing 14 games because of a knee injury, assisted on Eaves' goal at 2:17 of the third.
"He's an asset to our team and I think he played really well," said Emery, who made his seventh straight start one week after he had his fourth shutout of the season in a 3-0 victory at Boston. "He finds guys that no one else on the ice can find. He's just a special player, offensively."
Neil made it 2-0 at 7:48.
Glen Murray scored 56 seconds later, ending Emery's shutout streak at 135 minutes, 44 seconds. Antoine Vermette was awarded a short-handed goal with 45.1 seconds remaining after Boston's Marc Savard threw his stick to spoil the shot at an empty net.
The Senators were 11-2-1 while Spezza was sidelined.
"The team's been winning, we've been playing pretty tight defensive hockey and scoring a lot of goals, and I wanted to be a part of it," said Spezza, who hadn't played since Dec. 21, when he injured his knee in a 4-2 loss to Tampa Bay.
Tim Thomas made 34 saves for the Bruins, who were outshot 14-3 in the second.
Boston coach Dave Lewis praised Thomas' play in the second and his team's effort in battling to the end of the game, though he acknowledged that neither changed the end result.
"We need points," Lewis said. "There's no satisfaction in playing well now, you've got to get points. That's the disappointing part of it."
Eaves finally broke through in the third. After Spezza tipped the puck into the slot, Eaves spun and fired a low shot that went through Thomas' legs.
"It was a 0-0 game after two so it was anyone's game," Spezza said. "We knew we had a good second so we knew we had to keep working and get some chances. Tim Thomas is pretty unorthodox so you have to find a way to get some ugly goals on him."
Ottawa made it 2-0 moments later when Neil converted a pass from Peter Schaefer and beat Thomas to the glove side.
Murray scored at 8:44 on a setup from former Senators defenseman Zdeno Chara.
"We didn't play very well in the second period and they took it to us pretty good, and then they came on in the third and they got the first two goals," Murray said.
Boston had a power-play chance in the waning moments, but Savard belied the Bruins' frustration when he threw his stick at Vermette's attempt at an open net. Referee Kevin Pollock immediately pointed to the net, awarding the goal to Vermette.
"I'll take it, but it's not the same feeling," Vermette said about scoring a goal without actually putting the puck in the net.
Emery hadn't allowed a goal since Vancouver's Rory Fitzpatrick scored his first goal of the season 13:00 into the second period of Ottawa's 2-1 loss to the Canucks on Jan. 18. ... A sellout crowd of 19,846 attended the game.