"We gave that point away," Stars coach Dave Tippett said. "I don't think our goaltending was that great. I think (Turco) could have stopped a couple."
The Senators took a 1-0 lead when Alfredsson beat Turco with a wrist shot to the far side. However, the period ended poorly for Ottawa as Gerber allowed Niskanen to tie the game.
Ottawa made it 2-1 early in the second with a power-play goal as Vermette scored his first in 20 games.
The Stars got even again with a power-play goal of their own. Richards carried the puck from the side boards into the middle uncontested and beat Gerber glove side.
Dallas took the lead at the halfway point of the period on Petersen's goal.
With the Senators on the power play, Jere Lehtinen ran Alfredsson into the boards near center ice and the Ottawa captain was down on the ice in obvious pain. Alfredsson required assistance to get to his feet and was diagnosed with an undisclosed upper body injury. He will be re-evaluated Sunday.
The Senators managed to make something of that advantage as Spezza tied it by beating Turco at the side of the net.
"It was a real good game by our team," Ottawa coach Craig Hartsburg said. "I'm really proud of them. They played like a team, they battled, they worked, paid a big price and kind of fitting that Jason Smith scores the winning goal for us in a game like that. That's a huge win for our team."
Ottawa took the lead in the opening minutes of the third period with its third power-play goal when Picard beat a screened Turco.
"Even though bad things are happening you've got to stay in the moment and that's the way we have to look at every game," Turco said. "It's an interesting time right now."
Eriksson made it 4-4 with just over five minutes remaining in regulation, beating Gerber after a scramble at the front of the net.