Johnson's 18-footer with 0.7 seconds left in the second overtime lifted the Nets to a 115-113 victory over the Washington Wizards on Friday night.
Bradley Beal's two free throws tied the score at 113 with 9.1 seconds to play before Johnson, who had 18 points, hit the shot that improved Brooklyn to 4-1 under interim coach P.J. Carlesimo.
"That's what big-time players do. We put him in a good position to make the play, and he made the play," Carlesimo said.
Washington double-teamed Johnson as it had earlier in the game, but this time he knew it was coming.
"In that situation, man, I'd seen the double team coming and I just took one hard dribble and pulled up for a jumper," Johnson said.
"How many times we've been here? I've lost count," an exasperated coach Randy Wittman said.
After Martell Webster's jumper gave the Wizards a 106-104 lead to begin the second overtime, Gerald Wallace made a layup and Keith Bogans converted a three-point play and a layup for a 111-106 lead with 3:21 to play.
Beal hit a 3-pointer as the first overtime ended to tie the score at 104. It was the second time Washington extended the game at the horn. Nene hit a hook shot to tie it at 93 in regulation.
The Wizards scored the first eight points of overtime to take a 101-93 lead with 1:27 left, but the Nets later scored 11 straight for a 104-101 lead with 3.4 seconds left, before Beal's shot.
"Bradley kept us alive when we should have been dead and we never should have been dead to begin with," Wittman said.
"The thing that's disturbing is that we do the same mistake over and over again as you're closing the game out. When a guy's doubled, you have to move the ball."
It was the third straight win in overtime for Brooklyn, and Washington's fifth straight loss in OT.
"Just went down to the wire. There was nothing they were really doing that was killing us. We were neck-and-neck the whole time," Beal said.
The game featured the return of Andray Blatche, who was let go by Washington last summer after seven stormy seasons. The Wizards used the amnesty provision on Blatche, who was banished from the team by Wittman last March for poor conditioning.
Blatche was booed by the crowd when he entered with just under five minutes to play in the first quarter. Moments later, with the crowd still booing, he hit his first shot and then drew laughs when he tripped as he ran down the court. He had 13 points and 12 rebounds.
"I probably screwed up by not playing him more than I did," Carlesimo said. "There's a lot of people that would not have been able to handle the situation, the first time back. He didn't handle it. He thrived in it."
Blatche said he didn't care about the crowd's reaction.
"The thing is, the booing didn't affect me at all because I don't play for them. They're supposed to boo me, they're supposed to go against me," Blatche said.
The Wizards started off quickly, shooting 9 of 11 as they took a 20-10 lead with 6:27 to play in the first quarter and led 30-20 after one.
In the second quarter, Washington stretched the lead to 36-22 before the Nets hit four consecutive 3-pointers to cut the deficit to two. The Wizards led 55-52 at halftime behind 13 points by Nene and Crawford.
Washington G Garrett Temple had a career-high 11 assists. ... Brooklyn was without G C.J. Watson (bruised right knee) and F Kris Humphries (sprained left ankle). F/G Jerry Stackhouse returned after missing Wednesday's game at Oklahoma City with a sore right hamstring. ... Wittman was heartened by seeing all four of his injured players: G John Wall (left knee), G A.J. Price (broken right hand), F Trevor Ariza (left calf) and F Trevor Booker (right knee) at practice on Wednesday. "I didn't know we had 15 here. There for a while here, I thought this was an eight or nine-man squad," Wittman said. None were well enough to play. ... The Wizards' 113 points were a season high. Their two highest-scoring games came in double-overtime losses.