"We had a couple chances this year to have it, and to be able to have it, it's pretty cool," Flyers captain Claude Giroux said.
Defenseman Marc Methot scored at 14:11 of the second period for the Senators, who had not lost in regulation since Feb. 16.
The Flyers began the game trapped in their own zone, but the Senators were unable to take advantage. Both teams appeared sluggish through the first half of the opening period, trading shots but struggling to create quality chances.
A hard hit on Senators defenseman Mike Lundin by winger Harry Zolnierczyk midway through the first period jarred both teams to life. The hit resulted in a five-minute major and game misconduct for Zolnierczyk, who appeared to leave his feet as he made contact.
The play will automatically be reviewed by the league. Lundin did not return to the game.
Sens coach Paul MacLean said on Twitter that Lundin has a concussion.
"I think Harry's hit and my fight really got the team going and back into the game," Rinaldo said. "We took it to them."
After a scoreless first period, the Flyers made it 1-0 at 7:24 of the second period on Voracek's team-leading ninth goal. He powered past the Senators' defense to cut toward the net and beat goaltender Ben Bishop. Voracek now has 15 points in his last eight games.
Bishop had won his last four starts for Ottawa (12-7-3), posting a 1.69 goals-against average during the stretch. But the Senators have had trouble scoring on the road, and though Bishop stopped 39 of 41 shots, it was the Flyers who tacked onto their lead next.
Simmonds' goal came just four minutes after Voracek's, as the Flyers' winger took a pass from Brayden Schenn to beat Bishop and give the Flyers a 2-0 lead.
Across the ice, Flyers goalie Ilya Bryzgalov put in arguably his most impressive performance of 2013, stopping 33 of 34 shots and earning his 200th career victory.
"I thought the guys played hard today, we had lots of chances to score," Flyers coach Peter Laviolette said. "There are some things I'd like to tighten up defensively, but overall, the walkaway, we said before the game just because of their goaltending and the way they play defense that you know we have to get comfortable winning a 1-nothing game or a 2-1 game, you know that's what it came down to. The effort I thought was good, it was there, so it was a big win."
Both teams were 0-for-5 on the power play, but the Senators' penalty kill was particularly impressive despite the outcome of the game, killing off a late 2-minute Flyers 5 on 3 and nine total minutes of Flyers power play. Even MacLean made note of his team's effort while disadvantaged, calling his penalty-killers "excellent."
Senators right wing Daniel Alfredsson received a five-minute major and game misconduct for crosschecking Rinaldo, but Ottawa was able to keep it a one-goal game. The Senators have only allowed four goals on the power play while on the road this year.
"It was a chippy game, no question," Alfredsson said. "I think we took exception to some of their hits and felt like the referees didn't call everything that maybe they should have. We stuck up for each other, and obviously my five minutes kind of hurt us in our chance to get back, but they killed it off and we got really close at the end to tie it up."
Ottawa, however, was careless in the third period, taking several penalties and thwarting their chances to push the game into overtime.
"It's an unfortunate one," Methot said. "I thought we gave ourselves a chance coming into the third period, and then we ended up burying ourselves over again with penalties and what not. It's just the way it worked out today."
Giroux's six-game scoring streak come to an end. ... Simmonds recorded the game-winning goal for the second consecutive game. ... Schenn passed his points total from last year (18) with his assist on Simmonds' goal. ... Alfredsson's major was the second of his career. The first occurred on April 9, 2002 vs. Montreal. ... The Flyers had 22 shots in the second period, more than half their total for the game (42).
Information from The Associated Press was used in this report.