Redick and Paul sandwiched 3-pointers around a free throw by Griffin to stay ahead, 100-94.
Johnson's running bank shot pulled the Nets to 104-101 with 36 seconds to go, but Jordan dunked and the Clippers finished off the game at the line.
Brooklyn opened the third with 10 straight points, including back-to-back 3-pointers by Anderson, to go up 65-54.
The Clippers staged a furious rally, outscoring the Nets 20-2 in a run that had three 3-pointers — two by Redick and another from Mullens — for their first lead, 74-67, since the end of the opening quarter.
Redick scored 10 points and Mullens and Griffin added five each.
"If you're down you play with a better sense of urgency," Redick said. "You've got no choice but to make a run. We want to get to the point where we're playing with a sense of urgency for four quarters."
Griffin blocked Plumlee at Brooklyn's end and scored at the other end, getting fouled and hitting the free throw. Paul tossed up an alley-oop that Griffin threw down to ignite the sellout crowd.
But the Nets closed with a 9-2 spurt to trail 76-75 going into the fourth.
"I definitely saw a lot of heart," Blatche said. "We showed effort and came out with a lot of fight. We all chipped in in different ways. We were always aggressive on offense and defense. It was a learning experience for us."
The Nets led 55-54 at halftime after blowing nearly all of a 10-point lead while being outscored 10-1 over the final 2:12. Paul scored five straight points and his steal led to a fast-break layup by Griffin, who got fouled and made the free throw.
NOTES: Garnett and Lopez have ankle injuries; Pierce has a groin injury; and Williams sprained his left ankle in Friday night's overtime win at Phoenix. Reserve F Andrei Kirilenko was out with back spasms. ... In the Nets' six losses, they've been outscored in the paint. The Clippers had a 44-38 edge. ... Paul has had at least 10 points and 10 assists in 10 straight games to start the season. ... Nets F Reggie Evans had 11 rebounds against his old team. ... Former Clipper Shaun Livingston had 11 points.