Heaton joined Burnley in May 2013, after turning down a further one-year deal at Bristol City. He decided to stay in the Championship, and Burnley offered Heaton a two-year contract attaching him to the club until June 2015, with an option of a third year. A target of manager Sean Dyche while at Watford, Dyche's first Burnley signing was described as a "good technician" with a "great pedigree". Heaton immediately became the first-choice goalkeeper for Burnley following the departures of Lee Grant and Brian Jensen. He made his Burnley debut against Bolton Wanderers on 3 August 2013. On 24 August, he was the recipient of a rare technical caution (his second of the match) for handling the ball after releasing it whilst playing against Brighton, a match they lost 2–0. Heaton was a part of Burnley's defence that allowed only 37 goals, the fewest in the league, as Burnley returned to the Premier League for the first time since 2009–10. Heaton also picked up 19 clean sheets, the most by any keeper in the regular season.