On 16 August 2014, in Palace's first match of the new season away to Arsenal, Puncheon took a corner which was headed in by Brede Hangeland for the first goal of the game. He was sent off for his second booking in the 89th minute, after which Arsenal scored their winning goal. On 17 January 2015, Puncheon scored his third goal of the season and second in as many games against Burnley in a 3–2 away win. Crystal Palace had come from 2 goals down to claim victory to boost their survival hopes. Palace manager Alan Pardew praised Puncheon's performance, describing him as "the best player on the pitch by a country mile".