Less than 24 hours after going 0 for 5 in a loss to Boston, Douglas scored 23 points on 9-of-17 shooting in 31 minutes off the bench.
"I just keep shooting. I don't let that bother me. It's preseason," Douglas said. "I'm confident enough to know that I'll be in the gym, I work out, so if I miss five, I shoot the next one like I made five."
Washington rookie John Wall had 19 points, six assists and five rebounds in the building where he was the No. 1 pick in the draft, but he was sitting along with all the other starters as the backups decided this one.
After Landry Fields tied it for the Knicks with a jumper with 26 seconds left, New York got the ball back after a Washington miss. Ronny Turiaf found Douglas cutting to the hoop, and he made both after he was fouled.
Yi Jianlian missed a long jumper at the buzzer for Washington, which led by 11 at halftime and gave almost all of it back by the end of the third quarter.
"The main thing is that we have to have a better third quarter," Wall said. "We really have to have the same focus we had at the beginning of the game in the third quarter."
Washington was without Gilbert Arenas, who has a strained right groin that's also expected to sideline him Tuesday night in the Wizards' exhibition finale against Detroit.
The Knicks were sluggish in the first half after losing to Boston a night earlier in Hartford, shooting 37.5 percent and falling behind by 11. They surged back into it in the third quarter behind Stoudemire before the benches took over.
"First time we played back-to-back, I thought a couple guys just didn't have their concentration going on and we can just find that malaise that we've seen a little bit," Knicks coach Mike D'Antoni said. "But second half they competed. They got after it, and in this league that's half the battle if you just compete every night, so hopefully we can do that."
The Wizards shot 54.5 percent in the first quarter, taking a 25-22 lead when Wall sped down the court after a Knicks basket and was credited with a layup on a goaltending goal with 0.3 seconds left.
It was tied at 44 before Washington ran off the final 11 points of the second quarter. Kirk Hinrich and Blatche hit consecutive 3-pointers before Wall converted a three-point play. McGee blocked two shots during the burst, then capped the scoring for the half with a dunk for a 55-44 advantage.
Stoudemire scored 10 points in the third, helping the Knicks rally to tie it at 70 in the closing minutes before Washington took a 74-73 lead to the fourth, and neither team led by more than three in the final period.