He made his league debut for the club on 10 August 2013, in a 1–0 win over Charlton Athletic at The Valley, replacing Jason Steele for the last 12 minutes shortly after Lukas Jutkiewicz had scored the only goal of the game. A week later, with Steele still injured, Leutwiler made his first league start at home against Blackpool. He conceded after 83 minutes from Chris Basham but Marvin Emnes scored an equaliser in added time. Leutwiler's third and final league appearance of the season came on 23 November, in Aitor Karanka's first match in charge, away to Leeds United: in the last minute of the first half, Steele was sent off for a foul on Dexter Blackstock and Leutwiler was brought on at the expense of Emnes in a 1–2 defeat.