Stone, a local firefighter, was honored by family, friends and law enforcement personnel who stood across from the First United Methodist Church holding American flags and also carried his stone casket to a lone fire engine in front of the church.
The procession to a cemetery eight miles away was expected to include dozens more fire trucks, police cars and other emergency vehicles, the AP reported.
Stone and his 6-year-old son, Cooper, were at the Rangers game in Arlington on Thursday when left fielder Josh Hamilton threw a foul ball to them in the second inning. Reaching over the railing in an attempt to catch the ball, Stone fell headfirst about 20 feet onto the concrete below. Witnesses said Stone was conscious after landing, but was pronounced dead within an hour from blunt force trauma.
Stone, twice voted Firefighter of the Year by his peers, had been with the Brownwood department since 1993, according to the AP. He had risen to the rank of lieutenant, and also worked as a paramedic and as a rescue technician at Texas Motor Speedway. He was also involved in disaster relief following Hurricanes Katrina and Ike, as well as fighting wildfires.
Flags in the area have been at half-mast since Friday, with several wreaths and roses left in his memory at a monument outside the fire department.
"We're a small town," Brownwood mayor Stephen Haynes told the AP. "We're not [small] enough that everyone knows everyone, but we are small enough that everyone is impacted in some way. Everyone has a friend or family member who was close to that family."
Haynes also said there have been discussions of a permanent memorial to honor Stone.
Club president Nolan Ryan and vice-president Jim Sundberg were among Rangers officials who attended the funeral.
Hamilton said Monday that Stone's family was still in his thoughts and prayers.
"I know Mr. Stone's funeral was today, and obviously the organization is being represented at the funeral," Hamilton said. "Somebody asked me if I was going to go to the funeral. I didn't know it was today, and I didn't know Mr. Stone and his family. I don't feel it's my place to be in an intimate setting."
He did say he would reach out to the Stone family at an appropriate time.
"As far as the grieving process, I can't imagine what that family is going through. When everybody has had time, I will reach out to them. My family is still praying for their family."