Street had difficulties in the first half of the 2013 season, giving up 10 home runs in 26 innings through June 23. But he followed that with a streak of 20 scoreless innings from June 26 through September 3, earning the National League Player of the Week honor for the week ending September 8. Street appeared in 58 games in 2013, missing only a couple weeks in early June with a calf strain. He converted 33 of 35 save opportunities and posted a 2.70 ERA, striking out 46 and walking 14 in 56 innings.