Street was called up to the MLB at the start of the 2005 season. He became Oakland's closer when incumbent Octavio Dotel went down in May with an elbow injury that required Tommy John surgery. Street saved 23 games in 27 chances to go along with a 5–1 record, 72 strikeouts, and a 1.72 ERA. Only Mariano Rivera's 1.38 ERA for the Yankees was better among American League relievers. Street had 72 strikeouts in 78 innings pitched, and opposing hitters batted only .194 against him. He was rewarded for his effort by being named Rookie of the Year, as the third player in a row who had spent some time in the Athletics organization (after Ángel Berroa in 2003, and Bobby Crosby in 2004).