Jose Gilberto Rodriguez, 46, is a suspect in at least three slayings in the last week, with police calling him a "possible serial killer" at a press conference Monday night.
He was arrested Tuesday morning after a police chase in the Houston area.
Rodriguez may be responsible for at least five attacks in the area, three of which resulted in shooting deaths, police said.
The first attack, on July 9, was a home-invasion robbery where the victim survived.
Four days later, Pamela Johnson, 62, was found dead inside her home in northwest Harris County, police said in a news release. Her car, a 2004 Chrysler PT Cruiser, was stolen from her home and found abandoned the next day at nearby Willowbrook Mall.
When investigators reviewed surveillance video from the mall, they observed the suspect, later identified as Rodriguez, park the car and leave the scene.