Ottawa's captain scored twice, including the decisive goal in the dying minutes, as the Senators all but extinguished Winnipeg's post-season chances with a 6-4 win Monday.
"That's what you get if you don't defend," said Winnipeg head coach Claude Noel.
"If you want to get into a horse race with them, then this is how the game ends up."
With just six games remaining in the regular season, the Jets sit six points behind both Buffalo and Washington in the Eastern Conference. Those two teams play each other Tuesday night so that lead will increase to eight for one of them.
Winnipeg's checking was weak and turnovers and other defensive mistakes were costly. The Jets face New York Wednesday as they play their final six games of the season 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."
Noel said the Jets created plenty of scoring chances but that wasn't enough as they abandoned their checking game.
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 4-4.
But Alfredsson scored his second of the game just 24 seconds later to turn cheers into groans from the raucous crowd at MTS Centre.
"You were never out of the game the way the game was going," said Noel.
"But you tie it late like that you should be able at least get to a point where you get a point and potentially get it back again, but to give up a goal on your next shift, with your best players?"
He also gave credit to Ottawa netminder Craig Anderson, who faced 48 shots. Pavelec faced 35.
"Obviously, we got the win, that's really all that matters," Anderson said as Ottawa shored up its hold on seventh spot in the East and now sits at 88 points.
The Senators have a four-day break before they face the Flyers 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.
Chris Neil, Kaspars Daugavins and Kyle Turris also scored for Ottawa (39-28-10), while Milan Michalek added one into an empty net.
Winnipeg's Antti Miettinen had two goals and Kyle Wellwood also scored as fans screamed themselves hoarse trying to give the Jets (35-33-8) the home-ice edge that has made the difference so many times this season.
Neil got credit for the first goal in the final seconds of the first period, slipping in Jason Spezza's rebound right in front of the Winnipeg net.
Daugavins scored less than two minutes into the second, silencing the Winnipeg crowd briefly, but nine seconds later they erupted when Miettinen put Winnipeg on the board.
Wellwood tied the game at two from the right faceoff circle when Kane swooped around the net and fed 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 fed Turris, who slipped a soft one into an unguarded net.
But Miettinen returned the favour just 20 seconds later to tie the game back up at three 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 stoned by Anderson as he tried to get in close and failed to make a clean shot.
Instead it was Alfredsson who scored at just 2:54 after Erik Karlsson stole the puck near the Winnipeg blue-line, setting up the game's dramatic finale.
Notes — 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. . . . Alexander Burmistrov went to the bench late in the third after what looked like a slash.