The win was only the third in the last 14 games for the Bulls, who remain in contention for the final Eastern Conference playoff spot despite their 34-38 record.
They trail eighth place Toronto by a game and a half.
"JP's a pro," Bulls coach Vinny Del Negro told reporters after Pargo's surprise start in place of the injured James Johnson.
"He prepares well and understands his role," Del Negro said. "Guys respect the work he does."
Pargo, a guard, also had five assists and four rebounds and was credited by Del Negro for his solid defense.
"That's the way I've played my whole career," Pargo said. "That (the start) got my energy up. I've been getting a lot of opportunity and I haven't played well. I'm glad I came through."
Forward Taj Gibson added 22 points and 13 rebounds for his third successive double-double. He scored 14 points in the opening quarter, including 10 of Chicago's first 12 points.
Reserve center Joakim Noah contributed nine points, twice making dunks in 13 minutes of playing time.
"I feel a lot better personally," said Noah, who has been playing a limited number of minutes because of a foot injury.
His first dunk came in the third quarter after the Nets scored 14 consecutives points to pull within seven as the Bulls failed to score for almost six minutes.
New Jersey, the worst team in the NBA with a 9-64 record, lost for the 33rd time in 37 road games this season.
Their ninth win had come on Friday when they beat the Detroit Pistons 118-110 at home for their second consecutive victory.
"We really had to work hard for that win," said Nets guard Devin Harris.
"I don't want to make the excuse that we're tired, but we just didn't have the juice to start with tonight."
(Reporting by Gene Cherry in Salvo, North Carolina. Editing by Patrick Johnston)