The hosts, who dominated in terms of possession and chances, deservedly took the lead after 21 minutes when Fernando Navarro's low cross was met by Alvaro Negredo, who slammed home his sixth goal in as many games from close range.
Negredo could have doubled the lead moments later, but he fired high and wide from 18 yards.
Out of nowhere, Juan Ignacio Martínez's men levelled the scores on 28 minutes. Barkero caught the Sevilla defence napping with a disguised through ball and Arouna Kone finished powerfully past Javi Varas.
It was one way traffic in the second half but a hattrick of superb saves from Levante stopper Gustavo Munua helped retain his side's parity.
However, the brilliant Munua pulled of a stunning save, diving to his right, to ensure that Levante took a point, which kept them fifth in the table.