Jonathan Denver's father, Robert Preece, worked security on game days at Dodger Stadium, the Dodgers said.
Meanwhile, the father of the suspect Michael Montgomery, accused of stabbing Denver to death, said his son told him it was done in self-defense.
San Francisco police say Denver, 24, was with his father, brother and two other people a few blocks from the San Francisco Giants' ballpark late Wednesday when their group exchanged words with some Giants fans who were leaving a nightclub.
The exchange turned physical and Denver, who was wearing Dodgers gear, was stabbed to death.
"There is no rational explanation for this senseless act," the Dodgers said in a written statement. "The pain that this has caused his family and friends is unimaginable."
Denver attended the game with his relatives but left in the eighth inning of what turned out to be a 6-4 Giants victory. His attackers did not attend the game, police said.
San Francisco police said Michael Montgomery, 21, of Lodi, was arrested on suspicion of homicide. Another person, whose name was not released, was also taken into custody.
"One of the suspects during the course of the interviews (with detectives) made incriminating statements that give us the indication that he will be the person booked for homicide," Police Chief Greg Suhr told reporters.
"We're trying to figure out what we're going to do with the other suspect," Suhr continued. "The investigation is still ongoing."
Police said they were still looking for two more suspects.
But Montgomery's father said late Thursday that his son was jumped during a fight and he stabbed Denver in self-defense.
Marty Montgomery told the Lodi News-Sentinel that his son said by phone that Denver, who was wearing Dodgers apparel, yelled, "Giants suck," at Montgomery's friend who was wearing a Giants hat when Denver and others hit his son and their friends without warning.
Marty Montgomery said that during the fight, Denver hit his son over the head with a chair, and in self-defense, his son, Michael, stabbed Denver.
"It was a self-defense deal," Marty Montgomery said. "(Michael) got jumped. (Denver and friends) started swinging chairs and he stabbed (Denver). (Denver) mouthed off about the San Francisco hat. It wasn't even (Michael's) hat."
The father said he had been trying to reach his son on Thursday when he called him and told him about the fight.
"He's freaking out," Marty Montgomery said. "He's like, 'I saw him die in his dad's arms.'"
Michael Montgomery and a friend went to Marty's house right in order to get the Giants hat before they left for San Francisco Wednesday afternoon, his father said. They were going to attend a rave.
"If they didn't have the hat, they probably never would have been in this situation," said Marty Montgomery, adding that his son was not a passionate San Francisco Giants fan.
Fans of both teams expressed a range of emotions as they entered Thursday night's game at AT&T Park.
"I was a little bit scared at first but then I thought tonight will probably be the safest night at this ballpark, so I thought it was still OK to bring my son out to the game," said Clay Brust, a Dodgers fan from Reno, Nev.
Brian Chew, a Giants Fan from San Bruno, Calif., said the stabbing was unfortunate.
"It seems like the passion that exudes in some fans is really pointed in the wrong direction," Chew said. "We have bigger purposes in life than just orange and black, or blue and white."
The altercation several blocks from the ballpark was the second violent confrontation between Dodgers and Giants fans in the past several years to end in death or serious injury. Bryan Stow, a Northern California paramedic and Giants fan suffered a traumatic brain injury after two men dressed in Dodgers gear attacked him following the teams' March 31, 2011, game in Los Angeles.
Stow's family said in a statement that they were "horrified and deeply saddened" by Wednesday's violence. "Our thoughts and prayers go out to the family."
Denver, his father and his brother had left a bar around 11:30 p.m. - about 90 minutes after the game ended - when they exchanged heated words about the Giants-Dodgers rivalry with another group of people leaving a nightclub.
One of the members of the group was wearing a Giants hat, Suhr said.
A fight broke out, and no one was seriously hurt at first. But a second altercation occurred a few minutes later, Suhr said.
"We're not sure at this time who wouldn't let it go. It wasn't clear who started the second fight," Suhr said, but it ended with Denver's stabbing.
"Obviously, this is one of the most storied rivalries in baseball. That said, and I'm a big Giants fan, there is no place at these games for violence," Suhr said. "Nobody's life should be at stake whether they are at the game, leaving the game, whether it's six blocks away and an hour and a half after the game."
Police were canvassing the area Thursday looking for the weapon used to kill Denver and any surveillance video of the crime.
Denver was born in Los Angeles County but was living in Fort Bragg, about 170 miles north of San Francisco, according to public records. He and his brother came to San Francisco to meet their father for the game, said Cas Smith, the owner of North Coast Plumbing in Fort Bragg, where Denver worked.
"He was a hardworking kid," Smith told KNTV-TV.
Denver, who just started a job as a plumbing apprentice, did have two recent brushes with the law in Mendocino County, according to KGO-TV. He was arrested on suspicion of driving under the influence in July, and for public intoxication at the county fair this month.
Police said they didn't know if alcohol was a factor in Wednesday's stabbing.
In Fort Bragg, longtime friend Matt Gomes told KGO-TV that Denver was a die-hard Dodgers fan who "was a really great guy who would do anything for anybody and always put a smile on people's faces when he was around."
The Giants said in a statement that they would observe a moment of silence for Denver at Thursday's game and increase security around the ballpark.
"While details are still emerging, we want to be clear that there is absolutely no place in our community for this type of senseless violence," the team said in a statement.
Police, too, said they planned to have more officers on the streets, although they said their presence is already higher during Giants-Dodgers games.
The teams, which moved west in the 1950s - the Dodgers from Brooklyn and the Giants from New York City - are longtime, fierce National League Western Division rivals, and passions tend to run high when the teams play in both cities.
The Giants won the World Series last year and in 2010 but are poised to miss the playoffs this season. The Dodgers, on the other hand, were in last place just two months ago but clinched the division last week.
Violence has marred previous contests between the teams. In 2003, Giants fan Marc Antenorcruz, 25, was fatally shot by a group of Dodgers fans after a drunken argument at Dodger Stadium.
Stow, the paramedic beaten in a parking lot after the Dodgers' 2011 home opener, is still recovering from his injuries.
Two Dodgers fans are awaiting trial on charges in the beating, which sparked outrage and brought stadium security changes around the state and country.
Contributing to this report were Associated Press writers Lisa Leff, Jason Dearen and Haven Daley, and Sports Writer Janie McCauley in San Francisco; AP Sports Writer Beth Harris in Los Angeles; and researcher Rhonda Shafner in New York.