Sevilla have had a mixed run of late, falling 0-2 to Valencia in the previous round but managing to qualify for the Champions League quarter-finals for the first time in 60 years after beating Manchester United 2-1 on March 13, reports Efe.
This second straight defeat threatens Sevilla's hopes to finish La Liga in a position that qualifies the team for the European tournaments.
Leganes opened the scoring just four minutes before the end of the first half with a goal from Unai Bustinza.
Leganes midfielder Javier Eraso doubled the lead for his side in the 69th minute.
With just six minutes to go, Sevilla midfielder Pablo Sarabia was sent off after he was shown a second yellow card.
His teammate Miguel Layun narrowed the gap in the last minute, but it was too little, too late.
Leganes provisionally jump to the 12th position in the La Liga standings with 36 points, moving out the relegation zone.
Sevilla remain in fifth with 45 points, just one point ahead of sixth-placed Villarreal, who are set to host Atletico Madrid later on Sunday.
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