By 10 p.m. when the game was over, there were no problems reported.
Both teams took to the field before the game and Giants relief pitcher Jeremy Affeldt addressed the underlying tension.
"In honor of the rivalry, and in honor of the Stow family, we ask that you respect that rivalry and respect each other as fans," said Affeldt.
Monday night's game was dedicated to Stow. His friend and witness to the attack, Matt Lee, was there.
"It was not a Dodger fan thing. It was just a thug thing," said Lee.
"We need to be a little kinder to each other and just remember that this was just a game. I think they put it best, it's so competitive on the field, but when it's done, they leave it there. I think us as fans need to do the same thing," said John Stow, Bryan's brother.
The crowd seemed to take on a different mood.
"I don't want to say it's quieter, but it seems to be a little less rowdy. I noticed there's a lot less Dodger blue out," said Giants fan Zoe Herlihy.
"Just in case anything goes wrong, I got the Giants jacket and I'll rip off the hat. You got to be smart about these things," said Dodger fan Aldofo Salazar. He didn't think he would need his disguise though. "Everyone in the bay has been nice to me. Of course, you get some jeers, but it's all friendly, nothing bad at all. I haven't experienced anything negative whatsoever."
"So far so good, it's been good. Just being here, of course, you hear 'Beat L.A.,' but so far so good. No harassment. No nothing, it's been good," said Dodger fan Alex Padilla.
Extra police and security officers kept a cautious eye on the crowds inside AT&T Park, but San Francisco Police Chief Jeff Godown says problems are more likely after the game.
"Usually because they consume some alcohol, it's late in the evening, they've been here for three or four hours. Both incidents in Los Angeles were the same way," said Godown.
Some Dodger fans say the real problem is not the rivalry, but instead, a growing criminal element around Dodger Stadium.
Preparations before the game
Prior to the game, Jorge Costa, vice president of ballpark operations and in-house security, had this message for fans, "Don't cause trouble."
"There's an element of people who are bent on that and those are the people that need to be dealt with," said Costa.
There was as much security for this game as there was for the World Series -- 40 percent more than normal and that includes a beefed up police presence.
"We're going to be very pro-active. We're going to be out in the stadium, out at the parking lots and the exterior of the stadium," said SFPD Spokesman Officer Albie Sparza.
Police and the Giants were worried about this series and feared someone might retaliate for Stow's beating. The 42-year-old paramedic is still in a coma after being attacked by two Dodger fans. Fans are also concerned about violence.
Giants fan Rachel Toro said we should turn the other cheek. She said, "That's the best thing we can do is show the people that we're better than that."
Just to be safe, Dodger fan Marc Vega toned down his attire. He said, "I got a Dodger hat and shirt and I just kept it. I don't want to be too much in anybody's face cause right now, I'm the only guy I can see who's wearing blue."
Fundraisers for Stow
The Giants not only dedicated the game to Stow, but they also teamed up with AMR to raise money for his hospital bills.
"We'll have over 100 volunteers, paramedics and colleagues, friends of Bryan's, to collect donations for the Bryan Stow Fund," said Giants spokesperson Shana Daum.
Dodger Stadium held a drive-through fundraiser to give L.A. fans an opportunity to donate to Stow's fund and by the end of the day they had collected more than $61,000. Hall of Fame manager Tommy Lasorda donated $5,000.
Street closures are planned as part of the increase in security and will continue through the three-game series.. King Street will be closed around the ball park. Traffic will be limited on Third Street. There will be no traffic on Second Street between Townsend and King Streets. Only residents will be able to access Berry Street from Fourth Street. There will also be road closures in the South Beach-Mission Bay neighborhoods near the ball park.