Alcinas played with Carlos Rodríguez for the third time in the World Cup of Darts and they qualified from Group D courtesy of a 5–3 win over Italy. They then repeated their 2010 shock win over the Scottish pair of Gary Anderson and Robert Thornton this time 5–4 and played Richie Burnett and Mark Webster in the quarter-finals. Alcinas missed four match darts in his singles tie against Webster to lose 4–3, but Rodríguez beat Burnett by the same scoreline to mean a doubles match was needed to settle the tie. Spain took an early 2–1 lead but went on to be defeated 4–2. His best result in an individual event in the rest of 2013 was a last 16 loss to Robert Thornton in the final UK Open Qualifier.