Watson entered training camp slated as a backup for the first time in his career. He was signed to be an added weapon in two-tight end sets. Head coach Sean Payton named Watson the second tight end on the Saints' depth chart to begin the regular season, behind Jimmy Graham. In Week 4, Watson caught his first touchdown as a member of the Saints on a four-yard pass by quarterback Drew Brees during a 38–17 win against the Miami Dolphins. On October 13, 2013, he collected three receptions for a season-high 61 receiving yards during a 30–27 loss at the New England Patriots. He was inserted in the starting lineup against the Patriots due to an injury to Jimmy Graham. In Week 10, Watson sustained a concussion in the Saints' 49–17 win against the Dallas Cowboys. He remained inactive for their Week 11 victory against the San Francisco 49ers. He finished his first season with the Saints with 19 receptions for 226 receiving yards and two touchdowns in 15 games and seven starts. Watson saw a sharp decrease in production as the secondary receiving tight end behind Jimmy Graham and had his lowest reception total since his rookie season.