With security in and around Yankee Stadium increased in the wake of the Boston Marathon bombing Monday, the Yankees paid tribute to the Boston community before and during last night’s 4-2 win over the Diamondbacks at Yankee Stadium. The Stadium was bathed in respect when a moment of silence was observed before the first pitch. In between the third and fourth innings, “Sweet Caroline’’ a staple of the Red Sox at Fenway Park, blared over the sound system. A commemorative ribbon was displayed throughout on the scoreboard. “It’s important to recognize everyone that was involved,” Joe Girardi said. “When you think about that being a song that is a tradition there, it’s special to Fenway Park and the people of Boston, but we are behind them and put the baseball teams aside.” Cops outside the Stadium is not a rare sight as game time draws near. However, at 1:30 p.m. yesterday there was a rare uniform NYPD presence at the gates. Inside the Stadium, the number of bomb-sniffing dogs was increased. Because the Yankees are one of the marquee name in sports and play in one of the most prestigious ballparks, the players are security conscious. “I think about it all the time,’’ center fielder Brett Gardner said before the game. “There is a good security team here. They take care of us. You don’t have to worry about it, just go to the field and play.’’ Mark Teixeira lauded the Yankees’ team security for making the players feel safe at home or on the road. “The Yankees do a good job — Mark [Kafalas] and Eddie [Fastook] are big for us,’’ Teixeira said of the security department that travels with the team. “They do everything they can to make us feel safe and be safe.’’ The Yankees released a statement regarding the disaster in Boston. “Our thoughts and prayers go out to the victims and the families who were affected by the bombings and our respect and admiration go out to the police, medical personnel and first responders who acted so heroically,” it read. “We stand united with the participants, volunteers, staff and spectators of the Boston Marathon and the people of Boston. “While we do not comment on safety and security measures at Yankee Stadium, this has always been our top priority and the public can be assured we are working with all levels of law enforcement and our own security personnel to ensure a safe environment.”