"We had some problems playing these guys," Ovechkin said. "You feel good about yourself when you break through, especially after the last game we didn't play at all."
Washington improved to 4-4 since Dale Hunter took over as coach.
Pavelec made 27 saves for Winnipeg. The Jets had won five straight at home.
"It's a bad two points we gave that team," Winnipeg coach Claude Noel said. "We played the way Washington wanted to play. That's the sad part. They lulled us into this game that we thought we could be cute.
"We wanted to play a sideways game and not a north-south."
It was the third of six meetings this season between the Southeast Division rivals. The Jets beat Washington in Winnipeg and lost on the road in overtime.
Neuvirth was forced to make a number of big saves in the first period as the Jets outshot the Capitals 14-7 and had the lone power play.
Winnipeg had two more power plays in the second, but only put one shot on Neuvirth with the man advantage.
Washington, which also had a power play in the second, sent 12 shots at Pavelec, who was making his 27th start of the season.
Ovechkin, who was booed every time he touched the puck, didn't have a shot on goal until late in the second period.
The teams traded power plays in the third period, but the Jets didn't even get one shot on Neuvirth with their advantage.
The Capitals went ahead on shots on goal late in third, but Pavelec kept them out with a couple of big saves before Ovechkin's winner.
"It happened. I made a mistake," Pavelec said. "It was a pretty good game. Both teams could win. We could win the game. They took advantage in the last minute and made a good play so they scored a goal.
Jets forward Jim Slater played his 400th NHL game, all with the Winnipeg/Atlanta franchise. ... Ovechkin has up 65 points in his career against the Winnipeg/Atlanta franchise, more than any other team he's played against.