Then he got back at the team that released him five days before the start of last season, hitting a tiebreaking double in the ninth inning of the first game at Fenway Park since Boston won the World Series last October.
Getting released "was disappointing because I knew that they had a pretty good chance," Overbay said. "It's no hard feelings or anything. It was just a matter of trying to squeak in for a couple of weeks, anyway."
During a nearly hour-long pregame ceremony, Red Sox players received their rings for winning the club's third title in 10 years. But then the Brewers ended Boston's streak of wins in nine straight home openers.
"It was a special day for us," Boston's Will Middlebrooks said. "It was emotional. For all of the guys that were a part of it last year, it's a special journey we were on."
Khris Davis doubled off Mujica (0-1), who made his Boston debut, and took third when Scooter Gennett reached on a sacrifice bunt. Overbay doubled to right for a 4-2 lead, advanced on the throw and scored on Carlos Gomez's fourth single of the game. Aramis Ramirez added an RBI single.
Mujica was the St. Louis Cardinals' closer for much of last season, then lost that job last September and did not pitch in the World Series against the Red Sox. He signed a $9.75 million, two-year deal with Boston.
"They came out swinging against Mujica," Boston manager John Farrell said. "Knowing he's been in the National League Central, they're familiar with him. At the same time, Edward's had a lot of success against that lineup. Mislocated a couple of balls, and he paid for it."
Ryan Braun was 0 for 5 and was booed each time he came to the plate in his first road game following his 65-game suspension last season. Four days earlier, home fans applauded the 2011 NL MVP loudly during Milwaukee's season opener.
"I certainly wasn't anticipating a reception like I got in Milwaukee," Braun said. "I've had plenty of experience dealing with it and I think regardless of how challenging anything is, the more you deal with it, the easier it becomes to deal with."
Boston's winning streak in home openers was tied with Cincinnati (1983-91) for third-longest in major league history and ended behind 11 straight by the New York Yankees (1998-08) and 10 by Pittsburgh (1945-54).
"This is a really intimidating place to come," Brewers manager Ron Roenicke said. "The adrenaline that flows in this place is amazing."
Milwaukee took a 2-0 lead in the second on Jonathan Lucroy's first homer of the season and Gomez's two-out, run-scoring single.
Boston scored in the bottom half with the help of an error by right fielder Logan Schafer, who misplayed Grady Sizemore's single for an error that scored Mike Napoli. Middlebrooks homered in the third.
Brewers reliever Will Smith allowed two walks with two wild pitches but no runs or hits in 1 1/3 innings. ... New England Patriots quarterback Tom Brady attended the game. ... Milwaukee RHP Wily Peralta stumbled and fell as he ran to the third-base line when Brewers players were introduced before the game. "I didn't see him go down but that's what I heard. He had a dirty uniform when he came back," Roenicke said. "He's fine."... Before the game, there was a moment of silence as a tribute to Lt. Edward J. Walsh and firefighter Michael R. Kennedy. They died last week while battling a fire in a home less than two miles from Fenway Park.