The crash, involving a black Mercedes wagon and a silver Mercedes hatch, happened at Bonogin around 5pm on Friday.
It was just a kilometre from where police had tried but failed to flag down a black car being driven erratically, Queensland Police said.
Gold Coast District Officer Chief Superintendent Craig Hanlon said the officers opted not to pursue the car because of the alleged "conduct of the driver" and "it was too great a risk".
"A very short time later members of the public approached that police vehicle and advised that approximately a kilometre up the road ... that Mercedes had collided with another Mercedes, a silver car," he told reporters on Saturday.
The silver Mercedes was pushed into a power pole that fell onto the black car, which then caught fire.
The officers got a woman, named in multiple media reports as 46-year-old Uiatu "Joan" Taufua and the mother of Broncos player Payne Haas, out of the black car.
They got two of the three people out of the silver car and performed CPR before the ambulance arrived.
But all three - two women and one man, aged 70, 35 and 70 respectively - died at the scene. Police said they were members of one family.
Chief Superintendent Hanlon it was a horrifying scene.
The tragedy has lifted the state's road death toll to 296 for 2022, which is the worst year in a decade.
"The frustrating thing for police is, some of those lives lost could have been saved if people had done the right thing on the roads," he said.
Ms Taufua was taken to hospital where she was on Saturday in a stable condition with numerous fractures and other injuries.
Ms Taufua and the three victims were all locals.
While the crash is now under investigation, Chief Superintendent Hanlon said it was too early to say if and when charges would be laid.
The force's internal watchdog - the Ethical Standards Command - is also looking into the incident.
Witnesses and anyone with dashcam or CCTV footage of the crash or moments leading up to it are being urged to come forward.
The Brisbane Broncos declined to comment.