Crawford made only 9-of-26 shots -- his most attempts since his rookie season in 2010-11 -- but he had four of the Wizards' final five baskets.
"I just really wanted to do everything to take the win," he said. "I didn't care how many shots I shot. Turnovers. Nothing. I just wanted to do whatever it took to win."
Bradley Beal added 15 points for the Wizards, who trailed by as many as 13 and never led until the fourth quarter. Washington won for the first time on the road after losing its first eight away from home this season.
Ryan Anderson led New Orleans with 17 points but did not score in the second half, missing all nine of his shots after going 7 of 12 in the first half. Davis, who missed 11 games with a stress reaction in his left ankle, had 13 points and seven rebounds.
The game befitted the team with the worst record in the Eastern Conference (Washington) and the team with the worst in the West (New Orleans). The Wizards shot 32.9 percent, scored 11 points in the first quarter -- a season low for any quarter -- and had a season-worst 36 points at the half.
"That first quarter, I thought I was getting my teeth pulled at the dentist without any Novacaine," Wizards coach Randy Wittman said. "It was pretty painful."
The Hornets shot 32.5 percent and scored a season-low 10 points in the fourth quarter, losing for the 13th time in 15 games.
Crawford, normally a reserve shooting guard, started at the point for the first time because A.J. Price fractured his right hand against Golden State last Saturday and will be out four to six weeks. And Price was starting only because 2010 overall top pick John Wall has missed the entire season with a stress injury in his left knee.
"It was different playing the point," Crawford said. "At the beginning of the game, I was thinking about different stuff. Once I got into the game and once I saw what the team needed, I got comfortable."
His numbers weren't point-guard like -- he shot first and passed second, finishing with four assists -- but the Wizards will take it.
"It was good for the first time kind of starting there," Wittman said. "You could see him thinking. It's going to be a little bit of a process, but he came down the stretch and made big shots."
Crawford hit a 3-pointer to give the Wizards a 68-65 lead with 5:09 left, and he sank a tough leaner while drawing a foul from the Hornets' Greivis Vasquez the next time down the floor to make the score 71-65.
"We were stuck on 65-65, kept going back down," Crawford said. "They were missing, we was missing and I just wanted to get that shot to break the ice."
Davis responded with a dunk on an alley-oop from Austin Rivers, the Hornets' first points in nearly four minutes, but another attempted alley-oop from Vasquez to Davis resulted in a turnover that Nene converted into a layup as Washington went ahead 73-67 with 3:00 left.
Davis converted a three-point play in transition to cut the deficit to 73-70 with 1:51 to go, but the Hornets did not score again. After Vasquez missed a wild running hook with just over a minute left, Crawford hit an open 18-footer to put Washington ahead 75-70.
Anderson went 0 for 7 in the fourth quarter.
"I had some great looks," he said. "Those are shots I normally make, and I wouldn't turn them down again. I would shoot them over and over again."
Nene had a double-double for Washington with 10 points and 10 rebounds.
Rivers, a rookie starting for the first time in 10 games, had 11 points for the Hornets, but only two of them came in the second half.
The first two possessions for both teams set the tone. The Wizards turned the ball over on their first possession and missed their first shot badly. The Hornets clanked their first shot off the backboard and committed a turnover on their second possession.
At one point, the Wizards were 6 of 26 from the floor with almost as many air balls as made shots. Jan Vesely even shot an air ball on a free throw, falling to 3 of 15 for the season at the line.
Even with the return of Davis, who scored 28 points and grabbed 11 rebounds in his last game before getting hurt, the Hornets could not hold on.
"We did not play with the effort that is necessary to win an NBA game," Hornets coach Monty Williams said. "You don't deserve to win when you play that way."
It was the first NBA game since April 1, 2005 when both teams shot below 33 percent. The Hornets were involved in that one, too, playing the Houston Rockets. ... Davis entered with 4:34 left in the first quarter and played 24:54, just under his average of 26 minutes. ... With its first road win, Washington is ahead of its pace from last year, when it lost its first 25 games away from home.