Martin Erat scored the winner in the sixth round of the shootout on Tuesday, despite Washington being outshot 47-32 and giving up many breakaways to the hard-charging Jets.
"We made every mistake you can make basically in the course of the game," said Capitals head coach Adam Oates. "It's the first time this year where we've come to this building or a Canadian rink and the boys are so much faster."
He said they'll find things even faster in Edmonton, where the Capitals (4-5-0) play Thursday.
"It's the fastest rink in the league and you've got to be prepared for that. It's a mental adjustment."
Oates gave credit to goaltender Braden Holtby for stopping 43 of the 47 shots he faced in three regulation periods and five minutes of overtime. The Capitals managed only 32 on Winnipeg netminder Ondrej Pavelec, not even one in overtime.
"Holt made some huge saves," said Oates.
Alex Ovechkin had two goals and an assist for Washington, while Mikhail Grabovski and Troy Brouwer also scored.
"You notice it, it's hard not to," Holtby said of the barrage he faced, which included more breakaways than he could count.
"We got a win on the start of our road trip here and we've nowhere to go but improve for the rest of it."
Bryan Little struck twice for Winnipeg (4-5-1), while Grant Clitsome and Blake Wheeler also scored as the Jets wrapped up a six-game homestand, their longest of the season.
Andrew Ladd had three assists and coach Claude Noel was pleased at the way his captain's intensity helped lead the team.
"He played with a lot of will tonight, through physical play and winning battles," said Noel. "That's the Andrew Ladd that really helps us win."
Besides the point from the shootout loss, Noel was pleased with the Jets efforts, including coming back twice from deficits and getting more offence from his juggled forward lines.
"We wanted to play physical. I thought that we did. We got good production from our leaders. They stepped up and played and that's a good thing, so I think we go from there and build on that."
Oates said the Capitals will be talking about what they need to do as they move forward.
Although they were outhustled in the first, Grabovski opened scoring in the second period with his fourth goal of the season when he swept in and put a loose puck behind Pavelec at 3:11.
Little brought the Jets even with his first goal when he and Ladd broke away shorthanded at 7:21. It was the Jets' second breakaway of the penalty with Evander Kane failing to get past Holtby one-on-one.
"We just didn't finish," said Kane of the many scoring chances that didn't end up in the net. "It's a good sign to get those breaks and get those opportunities but it was a tough game (to lose) because we did a lot of good things."
Just just over a minute after Little's goal, Byfuglien fed Clitsome, who slapped in his first goal of the season in from the point to give the Jets the 2-1 lead.
Washington caught a break when Ovechkin broke away at 15:51 to beat Pavelec one-on-one to even it at 2-2.
Then Ovechkin was fed off the faceoff beside the Winnipeg net and slipped one through the crowd at 18:02 to give the Capitals the lead, although it didn't last long.
Wheeler tipped in a shot from Kane with less than a minute left in the period to even it up again.
Brouwer finally connected with a power-play goal just under five minutes into the third period. The Jets had successfully shut down the best power play in the NHL until then.
But Little evened it up again with a wrist shot from the slot at 7:04 as the Jets continued to carry the game to the Washington net.
Notes: The Jets and Capitals are well acquainted. Going into Tuesday's game, the Jets had a record of 4-4-1 against Washington since the start of their inaugural 2011-12 season in Winnipeg in the Southeast Division.