The Jets outshot the Capitals and created most of the best scoring opportunities, including a short-handed two-on-one thanks to Dustin Byfuglien.
Capitals goalie Braden Holtby had to deal with breakaways throughout the game and stopped some of Winnipeg's best shooters.
But it was Washington that beat Jets netminder Ondrej Pavelec first.
Grabovski scored his fourth goal of the season when he swept in and put a loose puck behind Pavelec at 3:11 of the second period, after Winnipeg defenceman Zach Bogosian failed to clear it.
Little brought the Jets even when he and Ladd broke away shorthanded with at 7:21. It was the Jets' second breakaway of the penalty with Evander Kane failing to get past Holtby one-on-one.
Then just over a minute later Byfuglien fed Clitsome, who slapped his first goal of the season in from the point to give the Jets the 2-1 lead.
Holtby dealt with shot after shot throughout most of the second but 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 with a wrist shot from the slot at 7:04 as the Jets continued to play much of the game in front of 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.