Real Madrid lost their second game in three days away to Sevilla, losing their privileged place at the top of the table, and leaving themselves dependent on what Atlético and Barça do in their last eight games of the season.
Los Blancos took the lead through Cristiano Ronaldo, only for Bacca to equalise two minutes later. The Colombian sealed the points after scoring from Rakitic's second-half counter-attack.
Tonight's was Sevilla's sixth straight win. Bacca was in fine goalscoring form and his brace sealed the home side's comeback after the Portuguese had given Real the lead.
Carletto's side had no answer for Sevilla's intelligent football and winning La Liga now looks to be an uphill struggle for them.