Chicago’s Viktor Stalberg slips the puck past Michal Neuvirth for a first-period goal. (Jeff Haynes/Reuters)

The Washington Capitals had everything to play for given their tenuous grasp on a playoff spot. They were plenty rested, too.

Still, they came out flat Sunday at United Center, spotted the streaking Chicago Blackhawks a two-goal lead, committed too many turnovers and fell, 5-2, as their margin for error in the Eastern Conference playoff race continued to shrink.

Just how bad was the Capitals’ start? They did not record a shot on goal until 3 minutes 58 seconds remained in the first period. When Mike Green finally fired a shot on Blackhawks goalie Corey Crawford, the capacity crowd mocked the visitors with a Bronx cheer.

“We gave them a little bit too much respect, not coming out with much jam in our game,” said veteran Mike Knuble, whose second-period tally was his second goal in three games. “Look up at the scoreboard three-quarters of the way through the first period, you’re down 12-0 in shots. You can’t come out like that this time a year. That can’t be acceptable in our room.”

The Capitals remained in sole possession of eighth place in the East, clinging to a two-point lead over ninth-place Winnipeg. The Jets lost at home to Carolina, 4-3, on Sunday night. Washington, though, remained five points behind Southeast Division leading Florida, which has played one fewer game.

Which made the Capitals’ sluggish first period all the more curious.

“We need to come out every single game playing desperate,” defenseman Karl Alzner said. “We didn’t even have enough desperation in the third [period]. We’re usually a team that goes, goes, goes. Maybe we got a little too relaxed after we had a few wins there and saw ourselves in a nice spot in the playoffs.”

Alex Ovechkin, who tallied his 30th goal late in the second period, added: “We can’t play like that, especially in that kind of a moment.”

Coach Dale Hunter gave the Capitals a day off from practice on Saturday to recharge after a hard-fought loss in Winnipeg the night before. But the move backfired against a skilled Blackhawks’ team that, despite missing concussed captain Jonathan Toews, had gone 6-1-1 in its previous eight games.

Chicago rookie Andrew Shaw scored the first of his two goals only 3:35 into the game when he inadvertently deflected Duncan Keith’s point shot with his shin pad. Shaw was actually attempting to leap over Keith’s shot when it struck him and bounced through Michal Neuvirth (24 saves).

About four minutes later, Viktor Stalberg showed the burst of speed that he’s known for when he blasted around Dmitry Orlov at center ice and created a breakaway. Stalberg deked Neuvirth in the crease and extended the Blackhawks’ lead to 2-0.

At the time of Stalberg’s strike, the hosts led in shots, 8-0. The Blackhawks led 12-3 at the end of 20 minutes.

Knuble cut the Capitals deficit to 2-1 moments into the second period, but Patrick Kane answered about five minutes later. The Blackhawks’ star capitalized on a chance created by a brutal John Carlson turnover deep in the Washington zone.

“It was turnovers from our back end,” Hunter said. “Our defense was turning the puck over and making bad decisions with it.”

Shaw’s first career two-goal game — his second goal came on a wraparound after he slipped Jeff Schultz behind the net — made it 4-1 midway through the period. Shaw entered the game with seven goals.

Ovechkin answered with a vintage goal 5:32 before the second intermission. The Capitals’ captain skated the puck nearly the length of the ice, put the puck between his own skates, whipped around Keith and fired a shot past Crawford to trim the Blackhawks’ lead to 4-2 and give the Capitals a chance going into the third.

That chance, however, was short-lived. The Capitals mustered seven shots in the final frame and finished with only 18, their lowest total in 14 games.

“We thought we had a good opportunity to come back and win the game,” said Troy Brouwer, who played in his first game here since being traded to Washington by the Blackhawks last June. “We just didn’t have that determination, we didn’t have enough push. We didn’t create many chances in the third period and, as a result, we were hemmed in our zone the whole time and didn’t any opportunities.”

Capitals notes: Braden Holtby was recalled from Hershey and backed up Neuvirth. Tomas Vokoun was sidelined by a nagging lower body injury that Hunter characterized as minor. . . .

Back in Arlington, Nicklas Backstrom skated for a sixth consecutive day as he attempts to return from a concussion that has sidelined him since Jan. 7.