The Nets were 0-4 on a six-game road trip that ends against New Orleans at Oklahoma City on Tuesday night.
"Hopefully, we can save the road trip," said the Nets' Jason Kidd, who had 12 assists. "Any win right now, when we've only got 17 or 18 left, is big."
"It's good to get back with a win," New Jersey coach Lawrence Frank. "I thought Vince played at an unbelievably high level, and obviously Mikki was huge, too."
Pau Gasol scored 19 points and Chucky Atkins and Rudy Gay had 17 apiece for Memphis, which remained the only team in the league without consecutive wins. The Grizzlies snapped a six-game losing streak with a victory at Charlotte on Saturday.
Carter had 17 points and Moore 15 in the first half to help New Jersey take a 51-45 lead at the break. Nachbar's layup with 8:05 left in the game push the Nets' lead to 99-81.
Memphis' return home after a three-game road trip was met with a sparse crowd, graciously put at 12,165.
Grizzlies Coach Tony Barone said he was disappointed with the Grizzlies' lack of energy.
"I don't have any explanation for us not playing with a sense of urgency," Barone said. "We didn't play with urgency all night or from the beginning of the game."
Barone said his efforts to put fire up the Grizzlies have not been successful.
"We tried to explain to them all the teams coming in are playoff teams. We aren't in the playoffs," Barone said, "but we want them to come in with some pride and make teams have to beat us."
The Nets are 12-20 on the road overall. ... The Grizzlies, in a slump after three straight trips to the NBA playoffs, dropped to 16-49 with the loss to the Nets. They were 36-29 at the same point last season. ... The Nets grabbed 13 offensive rebounds and outscored Memphis 19-9 in second-chance points. ... New Jersey shot 77.8 percent in the third quarter, while Memphis made 50 percent. ... The Grizzlies are in a five-game homestand, and host Cleveland on Wednesday.