On 26 March 2014, Bacca netted two goals in a 2–1 Sevilla victory against the then league leaders Real Madrid at the Ramón Sánchez Pizjuán Stadium. In the second leg of Sevilla's Europa League quarter-final tie with Porto on 10 April, he scored his side's third goal in a 4–1 win, securing a 4–2 aggregate victory and a spot in the semi-finals of the competition. Two weeks later, he scored the second goal in their 2–0 semi-final first leg win over compatriots Valencia. In the final on 14 May, he scored in the penalty shootout where Sevilla beat Benfica to lift the trophy. Bacca was voted by Marca as the best signing of the 2013–14 La Liga season. At the LFP Awards, he was voted the season's best player from the Americas, ahead of Real Madrid's Ángel Di María and Barcelona's Neymar.
On 30 September 2014, Bacca signed a contract extension with Sevilla, keeping him at the club until 2018. He scored seven European goals as the club retained their Europa League crown, including two in the final for a 3–2 victory over Dnipro Dnipropetrovsk, thus qualifying the team to the next season's Champions League.
On 31 May 2014, Bacca scored to put Colombia ahead 2–0 against Senegal, in a match that finished 2–2. Bacca was selected to the final 23-man roster for Colombia at the 2014 FIFA World Cup in Brazil less than a week later. Bacca made one appearance in the finals, coming on as a substitute and winning a penalty in Colombia's 1–2 defeat to hosts Brazil in the quarter-finals.
In a friendly match against El Salvador at the Red Bull Arena in Harrison, New Jersey on 10 October 2014, Bacca scored twice as Colombia won 3–0.