Trailing to Cristian Sapunaru's early goal, Barral – introduced in the 38th minute for the injured Baba Diawara – levelled proceedings on the stroke of half-time before netting a late winner.
Elche started brightly and took a deserved lead in the 26th minute after Sapunaru pounced on Botia's knock-down to sweep home following a clever free-kick.
And they should have doubled the lead in the 40th minute, only for Fidel – who was sent through on goal – to chip over Levante goalkeeper Keilor Navas and wide.
Levante made them pay immediately as Barral headed Nabil El Zhar's cross into the back of the net to equalise.
Both sides had good chances in the second half, with Richmond Boakye guilty of missing a sitter when he skewed wide from inside the six-yard box with an empty net to aim at following a corner.
And Levante again benefited from Elche's profligacy, as Barral fired a bullet header past Levante goalkeeper Tono following Pedro's cross in the 81st minute.
That was enough for Levante to win their first match in five and climb into the top half, while Elche remain 12th in the table.
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