Jonathan Denver, 24, was stabbed during a fight between two groups of men after the game. It happened at Third and Perry streets, near Harrison, just a few blocks from the ballpark.
Michael Montgomery, 21, from Lodi has been arrested and charged with homicide. His father claims his son acted in self-defense.
Chief Suhr says Montgomery made incriminating remarks to detectives. Another man is in custody and police are searching for two others in what they call, "a senseless tragedy."
Kristoff Fajardo left a blue candle at the scene where a fellow Dodgers fan was killed in an argument over the team's rivalry with the Giants.
The victim, a resident of the Mendocino County town of Fort Bragg, was decked out in Dodgers gear.
He left the game at AT&T Park in the 8th inning with his brother, his father, and two others, and headed to a local bar.
According to police, after the group left the bar around 11:30 p.m., they ran into four suspects on Third near Harrison. One suspect wore a Giants cap. Chief Suhr says those Giants fans did not attend the game and were leaving a nearby nightclub when their paths crossed and a sports beef turned deadly.
"There was an initial fight and nobody was seriously injured," Chief Suhr said. "Then that the fight stopped and for whatever reason one or more of the parties wouldn't let it go and that's when the stabbing occurred."
Police are now going door-to-door in the area, looking for the weapon and any video of the crime. Investigators say the car the suspects were driving is registered in Lodi.
We spoke with one of Denver's friends, who shared what may have been the last photo ever taken of the 24-year-old.
"He was a die-hard Dodgers fan," Matt Gomes said.
Gomes showed us a picture taken at Wednesday night's Giants-Dodgers game that shows Denver with his father and brother.
"I was just with his whole family," Gomes said. "We all just feel horrible for his mom and his brothers and just his whole family."
We spoke with a family member Thursday outside Denver's grandparent's house in Southern California. He says they're still in shock.
"The family is devastated, grandparents lost their grandson and Robert's driving home, the dad. It's his birthday today. His son died in his arms, I guess," said David Morgan.
Denver's father works as a security guard for the Dodgers. He was in the Bay Area visiting his sons for his birthday.
Denver had just started a job as an apprentice at the North Coast Plumbing, where his boss and coworkers told us he was a fine young man trying to find his path in life.
The 24-year-old did have two recent brushes with the law in Mendocino County; one for driving under the influence in July, and a second this month, which was a drunk in public arrest at the local county fair.
Police do not know if alcohol was a factor in Wednesday night's fatal fight. Denver had no history of violence and his friend told us the victim was probably trying to protect his friends and family.
When asked what people should know about him, Gomes said, "That he was a really great guy and would do anything for everybody and always put a smile on people's faces when he was around."
On Wednesday, the team released a statement saying, "There is no rational explanation for this senseless act which resulted in Jonathan's death. The pain that this has caused his family and friends is unimaginable. Words are not enough to describe our sadness."
SFPD spokesperson Sgt. Danielle Newman says the police department is concerned for baseball fans.
"We are concerned that that may have been what took place," Sgt. Newman said. "And based on those concerns, the department and the mayor want to make sure that everyone is aware that there's no place in San Francisco for that type of violence. The rivalry needs to stay out on the ball field; not in the stands, and not on the streets. So tonight, we have an increased police presence going out."
There were a lot of officers inside the stadium and on the streets. They were in uniform and under cover, dressed in Giants and Dodger gear. But all of that aside, everyone participated in a moment of silence in honor of Denver.
The Giants and Dodgers are longtime division rivals. The Giants were the defending World Series champions. But this year, the Dodgers won the division while the Giants were set to miss the playoffs.
The Giants issued a statement saying, "We were deeply saddened to learn of last night's horrific incident that occurred several blocks from the ballpark. Our thoughts and prayers are with his family during this difficult time."
The violence comes just three days after a teenage football fan was attacked at San Francisco's Candlestick Park during the San Francisco 49ers 27-7 loss to the Indianapolis Colts. Other violence broke out at the game on Sunday despite an increase in security. The stadium was also the site of two shootings, beatings and fights during a preseason game two years ago.
Stadium security and fan behavior also came under scrutiny when another Dodgers-Giants matchup saw a Northern California paramedic severely beaten. Brian Stow, a Giants fan, suffered a traumatic brain injury after a beating by two men dressed in Dodgers gear following the March 31, 2011, home opener between the teams.
Stow's family says he's still enduring physical pain and memory loss from a severe brain injury.
The two suspects in his attack are waiting to go to trial.
The Giants are holding a fundraiser for Stow. The team will donate $10 from each ticket sold in certain sections of AT&T Park at Tuesday, Thursday and Sunday's games to a fund setup for Stow.
(Bay City News and the Associated Press have contributed to this report.)