James missed his third consecutive game because of a sprained left index finger.
"Whenever you get an opportunity to play against this team without him, you have to make sure you go out there and get it done," Jefferson said.
He and Carter led the Nets on a 9-0 run to start the third quarter, opening a lead the Cavaliers were incapable of challenging.
"Richard obviously was really, really good tonight," Nets coach Lawrence Frank said.
Jason Kidd didn't even play the fourth quarter, finishing his night early with seven points, six assists and 10 rebounds.
Cavaliers coach Mike Brown, who rarely jumps on his team publicly, expressed disgust with its performance.
"I want to see them fight," Brown said. "I didn't see any tough or any grit as a team out there."
The Cavaliers have lost four straight and are 0-3 without their superstar forward, falling to 9-10.
"Tonight, I felt we gave in as a team," Brown said. "We gave in to whatever they were doing and we didn't fight back until late. I'm disappointed that we gave in the way that we did."
Drew Gooden agreed with Brown's assessment, saying the team has to find a way to compete without James.
"We can't just sit back and wait for him to get back and say we will be all right when he gets back," Gooden said. "We have got to do something now."
Brown wouldn't comment before the game on whether James' injury is taking longer to heal than first anticipated. He was hurt Wednesday in a loss to Detroit, when Nazr Mohammed slapped at the ball as James began to shoot.
New Jersey bounced back from a 118-95 loss at Detroit on Sunday and improved to 5-3 on the road behind Jefferson, who shot 11-for-18 from the field and 13-for-15 from the line.
Jefferson downplayed his scoring output.
"I'm not too concerned about that. I'm more concerned about us being consistent as a team," he said. "We had a nice win tonight, but 48 hours ago we played (poorly)."
Carter -- who was 7-for-13, including 3-for-5 from 3-point range -- hurt his lower right leg in the third quarter, but returned. He didn't think it was serious.
The Nets shot 51.5 percent and even got some offensive production from Jason Collins, who had a season-high seven points.
Shannon Brown got the start in place of James and sparked the Cavaliers early with some hustle.
He drove to the rim on a fast break, scored and took a hard foul, bringing James, wearing a light gray three-piece suit, to his feet courtside.
Brown finished with a career-high 20 points and four assists.
He replaced Devin Brown, who was ineffective starting in James' place the past two games, going scoreless in 21 minutes Sunday in a loss at Boston.
However, the result was the same for Cleveland.
The Cavaliers took a seven-point lead on Daniel Gibson's 3-pointer midway through the second quarter. But they couldn't keep up with the Nets and fell behind 47-43 at halftime.
The Cavaliers could soon get some help from high-energy big man Anderson Varejao if they elect to match a three-year offer sheet the restricted free agent signed with the Charlotte Bobcats on Tuesday. Varejao has held out all season waiting for a new deal.
|With LeBron James out, Richard Jefferson soaks up the attention with his 36-point night. (AP)|
|New Jersey (9-9) «||19||28||27||26||100|
|NJ:R. Jefferson 36 Pts
NJ:J. Kidd 10 Reb
NJ:V. Carter 7 Ast
|CLE:S. Brown 20 Pts
CLE:D. Jones 12 Reb
CLE:S. Brown 4 Ast
|Players of the Game|
|R. Jefferson, SF||37||11-18||13-15||2||2||1||36|
|V. Carter, SG||36||7-13||2-2||3||7||1||19|
|M. Allen, PF||34||5-7||0-0||9||4||1||10|
|J. Kidd, PG||30||3-8||0-0||10||6||0||7|
|J. Collins, C||25||2-6||3-4||4||3||3||7|
|E. Gill, SG||22||2-4||4-4||3||2||1||10|
|J. Magloire, C||21||3-4||1-4||7||2||4||7|
|B. Nachbar, SF||18||1-3||1-2||3||0||2||4|
|S. Williams, PF||14||0-3||0-2||8||0||0||0|
|J. Boone, PF||3||0-0||0-2||0||0||1||0|
|D. Armstrong, PG||Did Not Play|
|A. Wright, SF||Did Not Play|
|N. Krstic, C||Did Not Play|
|M. Williams, PG||Did Not Play|
|Complete Box Score|
|D. Gooden, PF||38||6-16||2-2||5||0||1||14|
|S. Brown, PG||37||8-16||0-1||4||4||2||20|
|D. Gibson, PG||35||6-16||1-1||6||4||4||17|
|Z. Ilgauskas, C||30||1-6||6-6||7||0||3||8|
|S. Pavlovic, SG||24||1-9||0-0||0||3||1||2|
|D. Jones, PF||28||3-4||3-4||12||1||5||9|
|E. Snow, PG||25||0-3||1-2||6||3||4||1|
|D. Brown, SG||18||3-10||2-3||1||1||3||8|
|D. Jones, PG||4||0-1||0-0||0||0||0||0|
|D. Nichols, SF||2||0-0||0-0||0||0||0||0|
|D. Marshall, PF||Did Not Play|
|L. Hughes, SG||Did Not Play|
|I. Newble, SF||Did Not Play|
|L. James, SF||Did Not Play|
|C. Simmons, SF||Did Not Play|
|Complete Box Score|