In the second ranking event of the season, Burns beat Ryan Causton 5–3, Chen Zhe 5–2, and Matthew Selt 5–2 to qualify for the main stage of the Australian Goldfields Open, held in Bendigo.&lt;ref name="2013/14"&gt;&lt;/ref&gt; He played world number two Mark Selby in the first round and led the match 3–0, before Selby levelled at 3–3. Burns won the next frame and had numerous chances to secure a shock win but was ultimately defeated 5–4. At the Welsh Open he had a 4–3 win over Yu Delu, before losing 4–2 to Matthew Stevens in the last 64. In the minor-ranking European Tour events, Burns dropped just two frames in winning four matches to reach the quarter-finals of the Kay Suzanne Memorial Cup, where he was beaten 4–2 by Jamie Jones. Burns ended the season outside of the top 64 in the world rankings which would have relegated him from the tour, however by being placed 44th on the European Order of Merit he has received one of the eight spots to earn a two-year main tour card for the 2014–15 and 2015–16 seasons which were available to non-qualified players.