The two 16-year-olds and a 15-year-old were arrested in the early hours of Saturday morning after a crash in Oldbury.
Cannabis and a knife was allegedly found in the car.
The police chase happened when officers spotted a Volkswagen car believed to be linked to an attempted burglary that happened in Halesowen on Friday night.
The vehicle had been reported stolen in a knifepoint carjacking on February 14 in the Weoley Castle area of Birmingham. It then failed to stop for police on Wolverhampton Road and was pursued.
Following a short chase, the car came to a halt when it crashed on Titford Road. Nobody was injured but the three teenage boys were arrested.
One 16-year-old was arrested on suspicion of burglary and robbery.
Another 16-year-old was arrested on suspicion of robbery, possessing a weapon and possessing cannabis, while a 15-year-old was arrested on suspicion of robbery.
All three have now been bailed.