Due in part to a back injury suffered by Yankees catcher Austin Romine, the Yankees traded Kontos to the San Francisco Giants in exchange for catcher Chris Stewart before the start of the 2012 season. He began the season with the Fresno Grizzlies of the Class AAA Pacific Coast League. After starting the season with a 2–0 win-loss record and a 1.71 ERA in 23 appearances, the Giants promoted him to the major leagues on June 10. Through August 14, he pitched to a 2.33 ERA and a 1.15 walks plus hits per innings pitched (WHIP) ratio in 26 games, becoming a reliable member of the Giants bullpen. Kontos got his first major league win in relief of Barry Zito, successfully recording 7 outs without allowing a baserunner. The Giants went on to win the game 6–4 against the Astros. Kontos entered the postseason for a second straight season and eventually won the 2012 World Series with the Giants in a four-game sweep of the Detroit Tigers.