He scored two goals in the third period to send the Senators to a 6-4 win over the Jets on Monday.
"That's what you get if you don't defend," Winnipeg coach Claude Noel said. "If you want to get into a horse race with them, then this is how the game ends up."
Evander Kane gave the Jets hope at 17:03 of the third period after the puck went in off his arm as he was pushed into the net.
The goal was reviewed but stood to tie the game at 4-all.
However, Alfredsson scored his second goal of the game just 24 seconds later.
Ottawa is seventh in the Eastern Conference with 88 points.
"Obviously, we got the win, that's really all that matters," goalie Craig Anderson said.
The Senators have a four-day break before they face the Flyers on Saturday in Philadelphia, and Anderson says they need to stay sharp.
"We've played hockey the last three or four nights, we've played some pretty good hockey, so we've got to continue that and make sure that we stay mentally focused this week and when the puck drops on Saturday we're ready to go," he said.
Winnipeg's Antti Miettinen scored twice, and Kyle Wellwood also scored for the Jets (35-33-8), who are six points behind Washington and Buffalo in the race for the final playoff spot in the Eastern Conference. The Jets have only six games remaining.
They face the New York Rangers on Wednesday as they play their final six games against Eastern Conference rivals.
"The Rangers are coming up, a hard team to play against. If we're going to play like that, they're going to kill us again," Jets goaltender Ondrej Pavelec said.
"It's pretty simple. I don't think this is the hockey that's going to take us to the playoffs. This the hockey like summer hockey, exhibition games."
Neil got credit for the first goal at 19:34 of the first period, slipping in Jason Spezza's rebound right in front of the Winnipeg net.
Daugavins scored at 1:53 of the second to make it 2-0.
Miettinen put Winnipeg on the board only 1:09 later with a power-play goal.
Wellwood tied the game at 2-all at 6:54 from the right faceoff circle when Kane swooped around the net and gave him the puck.
Spezza had just served the second of back-to-back tripping penalties when he set up Ottawa's third goal of the game. Pavelec went down, and Spezza passed to Turris, who slipped a shot into an unguarded net at 17:26 of the second. Pavelec finished with 29 saves.
But Miettinen tied the game at 3-all only 20 seconds later when Anderson was slow returning after leaving the net to clear the puck.
Less than two minutes into the third, Wellwood had a chance to score the go-ahead goal on a penalty shot but was stopped by Anderson, who made 44 saves.
Alfredsson scored at 2:54 after Erik Karlsson stole the puck near the Winnipeg blue line.
Winnipeg's Tim Stapleton failed to keep his scoring streak alive. He scored in the three previous games. ... Pavelec made his 12th straight start in the Winnipeg net.