During the 2011 NHL Entry Draft, Burns, along with a second-round draft pick in 2012, was traded to the San Jose Sharks in exchange for Devin Setoguchi, Charlie Coyle and a first-round pick in 2011. With a year still left in his contract with the Wild, Burns signed a five-year contract extension on August 1, 2011, with the Sharks; the deal would pay him $28.8 million over five years, with an average salary cap figure of $5.76 million. In 2013, after rookie defenceman Matt Irwin's acquisition by the Sharks, in March, Burns was moved to forward, where he scored 20 points in 23 regular season games. In the 2013–14 season, Burns played the first eight games of the season, but missed 13 games after October 21 due to sore gums. On November 21, Burns returned to the Sharks' line-up and scored a goal against the Tampa Bay Lightning in a 5–1 winning effort. On November 29, against the St. Louis Blues, Burns recorded his first career hat-trick in a 6–3 victory.