Police told Eyewitness News that they tried to pull over the parents around Homestead and Tidwell overnight because of a burned out light.
The couple sped off and finally stopped at Tidwell near the Eastex Freeway.
Officials say the parents tried to bail on foot, leaving their three kids alone in the car.
They were quickly caught.
Police say the parents had open warrants, but they did not go into detail on what they are for.
The children are now safe with their uncle.