Rose, Randall Hampton and Ryan Allen are being sued for at least $21.5 million by a 30-year-old woman.
Lawyers for the New York Knicks guard sought the mistrial on grounds that they were not given access to several text messages they call essential to their case until the player was on the witness stand in the civil trial.
Federal Judge Michael Fitzgerald described the situation as "careless" but ruled that the delay in providing the texts to the defense should not result in a mistrial.
Rose, Randall Hampton and Ryan Allen are being sued for at least $21.5 million by a 30-year-old woman who says they gang-raped her at her apartment in Los Angeles in 2013.
The three men deny the allegations, claiming the sexual contact that took place was consensual.
Lawyers for the woman claim the text messages show the plaintiff was unaware the men were coming to her apartment and that she had no intention of having sex with them.
Rose's legal team say the texts prove the opposite -- that the woman was a willing participant.
Rose, 28, testified on Tuesday that the plaintiff was "awake and alert" when he and his friends took turns having sex with her.
The woman testified last week that she was so intoxicated that she has only "flashes" of memory of the alleged rape.
Rose said that after a party at his house, the woman sent him a text message that read: "You need to come see me right now."
The former Chicago Bulls star said the woman greeted the men at her door and told them they could have sex with her "one at a time."
Lawyers for the plaintiff say their client was drugged by the men earlier in the evening and that she was unaware they had entered her apartment.
No criminal charges have been brought in the case, although a criminal investigation was opened when the woman reported the incident to authorities in 2015, around the same time she filed the lawsuit.
On Wednesday, the Los Angeles Police Department said the death a day earlier of detective Nadine Hernandez, who was part of the team investigating the allegation against Rose, appeared to be suicide and unrelated to the case.
Hernandez, 44, died in hospital after she was found suffering from a single gunshot wound to the chest in a home in suburban Whittier.
"Detective Hernandez was among several detectives working on the Derrick Rose case at the time of her death," the Los Angeles Police Department said in a statement. "At this point there is no indication that her case work had any connection to her death. The Rose investigation will continue unimpeded."