Police first spotted the 16-year-olds around 11pm at Ley Road and Darien. Officers said they tried to stop the car because its left front headlight was out.
The car took off and refused to stop, police said.
Police chased the car westbound on Ley, north on Homestead and then south on Homestead back to Ley. The car then went west on Crosstimbers, but the driver tried to make another U-turn and lost control.
Police say the driver drove onto the curb and into the median on Crosstimbers at Fountaine.
Both teens jumped out and ran away, officials said. The driver was caught and arrested immediately.
A K-9 unit tracked down the passenger in a nearby yard.
Police said the teens took the car from a family member and then went on a joyride.
There is no word yet on what charges they'll face.