Joel signed for fellow league club
Everton on 9 July 2013, rejoining former Wigan manager Roberto Martínez on a five-year contract for an undisclosed fee. On 26 December 2013, he played in home defeat against
Sunderland. Robles came on as a 24th-minute substitute for
Leon Osman, as starting goalkeeper
Tim Howard had been sent off for a professional foul. Joel was unable to save the resulting penalty, however, as Everton lost the game 1–0. Robles then made his first Premier League start for Everton against
Southampton three days later due to Howard's suspension, with Everton winning 2–1.
On 13 January 2015, in a penalty shootout at the end of an
FA Cup third round replay at
West Ham United, Joel saved from
Stewart Downing. When the shootout went to sudden death, however, Joel hit the crossbar while West Ham's goalkeeper, his compatriot
Adrián, scored to eliminate Everton.
Joel made his second substitute appearance in as many Boxing Days when Tim Howard was injured in a 0–1 defeat to
Stoke City. Despite a nervy start,
Joel began enjoying one of the best runs of form of his young career, including three consecutive clean sheets. He was relegated to the bench in favour of a healthy Tim Howard.