In qualifying for the World Championship, Wasley squeezed past Sydney Wilson 10–9 and then beat Rory McLeod and Mark Joyce both 10–6 to stand just one victory away from playing in the sport's biggest event for the first time. He played world number 16 Robert Milkins in a dramatic match that went to a respotted black in the deciding frame which Wasley potted to reach the Crucible. In the first round, Wasley caused one of the biggest upsets in the tournament's history by eliminating world number two Ding Junhui 10–9 after having trailed 6–3 at the end of the opening session. In the second round he fell 7–1 down to Dominic Dale and could never recover as he was beaten 13–4. Despite this run, Wasley could not quite reach the top 64 in the rankings as he was placed number 72, which would have seen him relegated from the tour. However, he received the fourth of eight spots available on the European Tour for non-qualified players to earn a new two-year tour card for the 2014–15 and 2015–16 seasons.