Before the start of the 2011–12 season, Dyer signed a new contract with the Swansea club that expired in 2014. Dyer was in fine form for much of the 2011–12 season, in which Swansea City had an impressive run for a promoted side in the Premier League. Dyer scored his first Premier League goal in a 3–0 win over West Bromwich Albion on 17 September 2011. In a 3–1 victory over Bolton Wanderers, Dyer's pace and trickery on the field were extremely effective and earned him praise from his coach, Brendan Rodgers. Dyer contributed to a 3–2 victory over Arsenal by winning a controversial penalty and by scoring a goal, his third in three matches (including goals in a 4–2 win against Barnsley that sent Swansea to the next round in the FA Cup, and in a 2–0 victory over Aston Villa). Dyer earned press attention in the 3–2 win over Arsenal when Arsène Wenger accused Dyer of purposely diving onto the ground to draw a foul. On 3 March 2012, Dyer received a red card for a foul on Jordi Gómez during a match which resulted in a 2–0 win over Wigan Athletic. After the match, Dyer defended his tackle, stating he was not a 'malicious player', but the league suspended him for three matches. On 14 April 2012, Dyer scored in a 3–0 win over Blackburn Rovers, bringing his league goal tally to four for the season. On 24 April 2012, Dyer scored his fifth goal of the season and set up another goal for Danny Graham in a match that ended in a 4–4 draw against Wolverhampton Wanderers.