Video from SKY 4 showed the silver car mangled and upside down in the 1700 block of 14th Street around 11 a.m. Thursday.
Police said a woman reported the car stolen and called 911 when she spotted it in the area.
Officers tried to pull the driver over for a traffic violation and he took off.
The driver lost control at an S curve, hit an SUV and then the car flipped.
Officers pulled the suspect out of the car and he was taken to the hospital in police custody.
The driver of the SUV was not hurt.
Police say the car originally had been in Garland, warming up in the owner's driveway, when it was stolen.
"It's very unusual for people to spot their own vehicle," said Plano PD spokesman David Tilley. "Especially the same day, if at all!"
Allison Berry was working at a law office in downtown Plano at about 10 a.m. Thursday when she heard a commotion. She ran to the window.
"I saw this car just fly by and come into oncoming traffic," said Berry. "I swear, he must've been going 90 miles an hour."
Andrew Strong works in the same office as Berry.
"We all heard like a thump and thought, ‘What was that?'" said Strong.