Elliott stopped 26 shots -- including a spectacular glove save on James van Riemsdyk with 3:55 remaining -- for his fifth shutout of the season. He made 29 saves Monday night in a 2-0 win at Montreal as Ottawa ended a five-game losing streak.
"He's played unbelievable the last two games and we've been able to score the first goals, too, in the last two games, which definitely helps," Alfredsson said. "We're skating much better. We're being more aggressive, not as passive as we were. Hopefully we can continue that."
Kelly scored midway through the first period. Alfredsson put the Senators up by two with his 18th goal 18 seconds into the third.
Ottawa strengthened its hold on fifth place in the East with 83 points, four ahead of Philadelphia and Montreal.
Flyers left winger Simon Gagne got 19 minutes in penalties in the wake of Alfredsson's goal when he jumped Anton Volchenkov after the Senators defenseman checked him into the boards from behind earlier in the play.
"That's a dangerous hit," Flyers coach Peter Laviolette said. "The hits from behind are supposed to be called. [The referee] said he didn't get a look at it."
Gagne got a double minor for instigating a fight with a visor, a major for fighting, and a 10-minute misconduct.
"In my head it was dangerous," said Gagne, who acknowledged he was particularly upset the Senators scored on the play. "I was expecting a penalty on their side. It was a hit from behind. It's not part of the game and it shouldn't happen."
Volchenkov was given a roughing minor.
"I like to play physical, but I like to play clean physical," Volchenkov said. "Sometimes maybe dirty, but that's hockey."
The Senators failed to score on the ensuing 7-minute power play.
Brian Boucher made 24 saves in his fourth straight start for the Flyers, who lost their third in a row.
"It's got nothing to do with the referees," Flyers defenseman Chris Pronger said. "We had a 5-on-3 we could have scored on. We had a number of power plays there in the third we could have scored on. It's certainly not the referee's fault."
Philadelphia, tied with Montreal for sixth place in the Eastern Conference with 79 points, lost leading scorer Jeff Carter to a broken foot in Sunday's 3-1 loss to Atlanta. Carter is out for three to four weeks after he was struck by a shot. The injury ended Carter's streak of 286 consecutive games played -- the third-longest in team history.
The Senators had an anxious wait during a lengthy video review following Elliott's stop on van Riemsdyk. The review ultimately upheld the referees' ruling that the puck had not crossed the goal line during a pileup in the crease earlier in the play.
"It was a little bit long," Elliott said. "That's almost a good sign when it takes a little bit longer because they don't know if it's in or not so you just try to keep your legs moving and not think about it too much."
Ottawa, which went 0-for-7 with the man advantage, had already failed to convert three power-play opportunities when Kelly opened the scoring midway through the first. The Senators center held onto the puck on a 2-on-1 rush with Andy Sutton and fired a wrist shot past Boucher from the right side 10:34 in for his 14th goal.
Boucher made a strong glove save on Nick Foligno in the second just moments after the Flyers killed Ottawa's fourth power play.
Kelly was called for hooking Gagne 9:06 into the second just as Volchenkov drove Daniel Carcillo into the boards when the Flyers left winger carried the puck along the right side.
Philadelphia failed to score despite enjoying a 5-on-3 advantage for a full 2 minutes when Sutton was sent off for roughing Carcillo at 15:26. A delayed penalty had already been signaled against Erik Karlsson, who tripped Carcillo in retaliation for a hit in the corner.
Gagne had a great scoring opportunity late in the period, but shot high after Elliott slipped and fell.
Referee Bill McCreary immediately waved his arms to signal no goal when the puck ended up in the net 2:23 in after Foligno swatted it past Boucher with his glove. ... It was Elliott's sixth career shutout.
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OTTAWA - MARCH 23: Brian Elliott #30 of the Ottawa Senators stretches during warmups prior to a game against the...