Police say the chase began when Jatinderjit Kaur Mann wouldn't obey orders to stop the BMW he was driving.
Reporter Sherm-Min Chow of CBS affiliate KHOU in Houston reports that the BMW hit speeds as high as 130 mph.
"God dang, he's hauling. Wow. He is going fast!" observed a news helicopter following the BMW.
So fast, police couldn't keep up.
Police tried but failed to cut off the BMW as it swerved across highways, narrowly missing cars and motorcycles.
Then the car headed up an entrance ramp in the wrong direction. It avoided four vehicles, then slammed into a Dodge Stratus, almost directly head-on.
"We couldn't get away," the driver of Dodge, Diana McShan, later told reporters. "We couldn't swerve away. He rammed right into us."
The baby's grandmother was also in the Dodge.
After the collision, McShan jumped out of her car and slammed her fist on the BMW in disgust. Then she frantically tried to get her baby out of the backseat of the Dodge.
She had known all about the chase before she was hit.
"We had been listening to (news accounts of) it (on the radio) the whole time, but we didn't know where he was," she said. "I just happened to look up and saw the helicopters and said, 'He's got to be close.' That's when that happened."
Chow says police pulled the BMW's driver through its sunroof, adding he was apparently involved in some sort of incident at a restaurant before the chase began. His passport indicates he is a British citizen.
The man, recently divorced, was speaking incoherently to officers after his arrest, police say.
The grandmother wound up trapped behind the steering wheel. An ambulance took her, the baby and McShan to a hospital, where they were treated and released.
The suspect appeared in court Thursday morning, and was charged with aggravated assault and evading arrest.