The forward was introduced as a substitute on 38 minutes, and struck before the break to equalise for the hosts following Cristian Sapunaru's opener.
He netted his second 10 minutes from time, trebling his tally for the season in the process, to secure Levante a victory which sees them leapfrog their opponents and climb to 10th in the Spanish top division.
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Alberto Botia won the knockdown from a free kick, teeing up his fellow defender Sapunaru to confidently sweep home with his right foot for his first goal in a season in which he has only played four matches.
It proved to be a costly miss as Barral, an injury replacement for Baba Diawara, made an immediate impact, heading former Liverpool winger Nabil El Zhar's cross powerfully beyond visiting stopper Tono.
Both teams had chances to move in front, with Tono saving well from Nikos Karabelas while Boakye was even more wasteful for Elche, skewing an effort wide from four yards as the ball fizzed across the box.
Again, Fran Escriba's side were left to rue their wastefulness as Barral struck the winner with another header, Pedro this time the provider with a cross that the 30-year-old guided into the roof of the net.