Robinson finished with 12 points in his second straight start in place of Hinrich.
Thibodeau said Hinrich "made good strides" and the Bulls are "hopeful" he'll be ready.
James came down 1-on-1 against Hinrich in the opening quarter, and the players collided.
Both times they were missing point guard Kirk Hinrich, this time with a right foot injury.
The offense was a bit out of sync, too, and Hinrich could have helped in both areas.
The dunk was with such force, Hinrich found himself flinching to get out of the ball's way.
The Bulls also got a big performance from Kirk Hinrich, who finished with 18 points and 14 assists.
"We need to play well these last two games and get as healthy as we can be, " Hinrich said.
But the Bulls will miss Hinrich's defense against Nets point guard Deron Williams.
"We've dealt with injuries all year, " Hinrich said at the Bulls' morning shootaround.
That's when Deng answered with a 3-pointer from the wing and Kirk Hinrich brought the crowd to its feet with a floater.
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Hinrich warmed up in hopes of playing before he was ruled out.
Nate Robinson had 20 points and eight assists starting in place of point guard Kirk Hinrich, who bruised his left calf in Saturday's game.
Hinrich was hurt during Saturday's 142-134 triple-overtime victory, playing through the injury to finish with 18 points and a playoff career-high 14 assists in 60 minutes.
They couldn't match the effort of the Bulls, who played harder to make up for the absences of starters Luol Deng and Kirk Hinrich during the series.
The Bulls looked impossibly unlucky as the series went on, dealing with a team-wide flu bout and missing key players Luol Deng and Kirk Hinrich at times.
He cited two specific plays he thought merited flagrant fouls, one involving Kirk Hinrich in the first quarter and another by Taj Gibson late in the fourth.
Point guard Kirk Hinrich might miss his second straight game because of a bruised left calf, and Luol Deng and Taj Gibson were sick Wednesday and stayed home.
The way he was hobbling around, Hinrich hardly looked like a player who was about ready to suit up even though he said he has seen some improvement.
Nate Robinson had 12 points and 11 assists but shot just 4 of 16 in place of Hinrich, who returned to Chicago to get his right elbow examined.
The Nets simply had every advantage over a Bulls team that was without starters Kirk Hinrich (calf) and Luol Deng (illness), not to mention former MVP Derrick Rose (knee).
Hinrich may have been in position to actually draw an offensive foul on that play, but wrapped his arms around James' back and appeared to pull him to the ground.
Robinson started his second straight game and finished with 18 points, but it's no secret that the offense runs smoother with Hinrich and that he does a better job containing Williams.
And on the following possession, the Bulls took their first lead since the first quarter when Kirk Hinrich rebounded his own miss, then found Rip Hamilton for a triple to make it 85-84, Chicago.
The Bulls stood their ground even though Hinrich missed his second straight game with a bruised left calf, and Deng got sent home from the arena with flu-like symptoms, forcing coach Tom Thibodeau to shuffle the lineup.
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