Tyler Morris, 25, who works at the Lake Cities Fire Department near Dallas, was at Tuesday night's game with fellow firefighters when he fell over a second-deck railing onto field-level seats below.
He suffered a head injury and sprained ankle but no internal injuries, and was expected to be released from the hospital soon, friends said.
"Everything was happening so fast," said Kevin Conner, who attended the game with Morris. "The ball went over us and bounced off the seats ... and he went toward it. Then he flipped all the way around but grabbed onto the railing (before falling). That's what saved his life."
Conner said Morris had not been drinking at the game.
After Texas' Nelson Cruz hit the foul ball in the fifth inning of the game against the Cleveland Indians, the crowd gasped loudly, cried "Oh!" and stood up after Morris fell. Players and fans appeared worried and somber, and the game was delayed about 15 minutes as paramedics treated Morris and transported him to a Fort Worth hospital.
Four people struck when Morris fell were treated at the ballpark for minor injuries.
Morris, described by friends as outgoing and kindhearted, was still a bit shocked Wednesday but was talking and making jokes, his friends said.
"Tyler's used to being the person that helps other people, and now he's in the position of needing help," said Ben Westcott, a close friend and firefighter in the Fort Worth suburb of Watauga. "He said he's thankful to be alive, and he knows he's lucky."
Ryan, the Hall of Fame pitcher and Rangers' president, said Morris welcomed his visit and was "thrilled" to receive the foul ball he tried to catch.
Ryan said the incident "hasn't lessened his enthusiasm for the Rangers."
Ryan said the ballpark's railings were 30.25 inches tall, higher than the required 26 inches. He said the facility did not plan to raise the height of the railings.
"So we feel it was strictly an accident, an unfortunate thing that happened," Ryan said at a Wednesday news conference. "It's pretty hard to guard against something of that nature."
Some railings had been raised following a 1994 incident after the Rangers' first game at the ballpark. A woman posing for a picture suffered multiple injuries after falling 35 feet, but Ryan said that incident was not related to the railings.