In a 4–0 win over St Johnstone in the League Cup semi-final at Tynecastle, Hayes scored twice to help send the Dons into their first major cup final for 14 years. A poor goal kick by Steve Banks allowed Adam Rooney to square the ball across the six-yard box for Hayes to knock into the net. Clever footwork by the winger late in the second half led to a fine finish just inside the 18-yard box to wrap up the match and send Aberdeen through to the final. Celtic goalkeeper Fraser Forster's run of clean sheets (13 games) was finally ended on 1,256 minutes on 25 February 2014 when Hayes beat him from 30 yards to open the scoring in a 2–1 win for The Dons. The goal was later voted as the SPFL Goal of the Season. On 16 March 2014, Hayes started for Aberdeen in the League Cup Final but early on he suffered a shoulder injury and had to be replaced by Cammy Smith.
On 29 December 2014, it was announced that Hayes had signed a contract extension, keeping him at Aberdeen until summer 2018.