Hinrich sat out a 96-89 victory at Philadelphia on Wednesday after bruising his left knee against the Los Angeles Clippers on Tuesday and is day-to-day.
While Hamilton (foot) has missed six games and isn't expected to return until the end of the month, the Bulls have received some major contributions from their replacements.
Nate Robinson scored 14 points as the starter in place of Hinrich against the 76ers. Marco Belinelli added 16 and has averaged 16.8 per game since moving into the lineup at shooting guard.
"There's a lot of basketball left and we have to keep playing like this," center Joakim Noah said after scoring 21 points. "We had everyone here contribute. That's what you need."
Noah may not need to defend Brooklyn's leading scorer Brook Lopez on Saturday.
While Lopez was back in the starting lineup Friday after missing seven games with a sprained right foot, coach Avery Johnson said he would be re-evaluated before the team determines if he'll play versus the Bulls.
Lopez scored nine points in 24 minutes in a 107-105 double-overtime victory over Detroit after the Nets (13-9) went 2-5 in his absence.
Andray Blatche had 16 points off the bench and is likely to fill in again after averaging 17.6 in the seven games Lopez missed.
The Nets' defense, however, seemed to take a bit of a hit without Lopez, who ranks among the league leaders with 2.5 blocks per game after recording three on Friday.
Brooklyn has given up 94.3 points per game this season, but allowed 99.9 during the stretch without Lopez.
The Nets followed a five-game win streak with five consecutive losses before rebounding to win 94-88 at Toronto on Wednesday and a buzzer-beater at home on Friday.
Joe Johnson made a jumper from just inside the arc as time expired in the second overtime to give Brooklyn the win after blowing a 17-point lead.
"The coaches and, like I say, my teammates have the confidence in putting the ball in my hands down the stretch, then I have to come up big for us," Johnson said.
Johnson finished with 28 points and has 51 on 19-of-36 shooting in back-to-back wins.
Brooklyn has shot 47.6 percent from the field in its last three games, but is likely to find the going much tougher against the Bulls.
Chicago has allowed 88.2 points while holding opponents to 41.4 percent from the field in winning seven of 10. The Bulls rank near the top of the NBA in both categories.
Carlos Boozer will try to bounce back after finishing with five points on Wednesday. He averaged 18.0 points on 64.7 percent (22 of 34) from the field as the Bulls won two of three against the Nets last season.
Chicago has won eight of 10 at the United Center in the series, but the Nets took the last meeting, 97-85, on Feb. 18 behind 29 points from Deron Williams.