The Swans defended resiliently for large periods of the second half but could have extended their lead, and eased the growing tension around the Liberty Stadium, had Llorente and Leroy Fer done better with promising chances amidst the Everton pressure.
Swansea, who have 35 points, face bottom-of-the-table Sunderland and West Bromwich Albion in their final two games while Hull, on 34 points, play Crystal Palace and finish with a difficult game against Tottenham Hotspur.
Everton sit seventh with 58 points from 36 games.
(Reporting By Tom Hayward, editing by Pritha Sarkar)
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