She had learned of the shooting deaths of nine people in Charleston, South Carolina, after she left her North Carolina church Wednesday night.
She saw the people on TV praying, asking God to help someone find the killer.
Dills, hundreds of miles away, believes God used her to answer those prayers.
The 51-year-old woman was driving along a four-lane U.S. highway about 10:30 a.m. Thursday when she spotted Dylann Roof driving a black Hyundai toward the town of Kings Mountain.
"I don't know what drew my attention to the car," she told CNN's Don Lemon. She saw it had a South Carolina license plate. "In my mind I'm thinking, 'That can't be.' ... I never dreamed that it would be the car."
But she thought the driver was the same man whose photos had been on the news as the suspect. She called her boss at the florist shop, Todd Frady, and told him she thought she might be following the alleged killer. She pulled off the road to ask Frady what she should do.
He got on the phone with the Kings Mountain police while Dills started driving again in an attempt to catch the Hyundai so she could report the license plate number.
She caught up with Roof at a stoplight and was right behind him.
"I was very nervous," she said.
Roof continued west on U.S. 74 into Shelby. Dills had now been following the suspect for more than 30 miles. Shelby police caught up with Roof, pulled him over and took him into custody.
Dills told the Shelby Star
that she was late for work Thursday. It put her in the right place to answer the prayers of the people in Charleston, she said.
She told CNN she was a vessel through which God worked.
"It was Him from the time I left my house this morning. It was Him that made me look at that car. It was God who made this happen," she told Lemon. "God heard the prayers of those people."
Roof never adjusted his speed or driving she told the Star.
"He wasn't doing anything abnormal," she said. "He wasn't driving slow. He was just driving. He just kept going."