They lost defender Cristiano Piccini to a serious injury later in the first half and Levante equalised against the run of play in the 56th minute when Valencia's Carlos Soler clumsily diverted a corner into his own net.
Valencia's record signing Goncalo Guedes immediately restored the home side's lead down the other end by lashing into the far corner, while Mina scored a tap-in six minutes later to seal the three points.
Valencia are sixth in the standings after 32 games on 49 points, two behind fifth-placed Getafe who drew 2-2 at Valladolid and three back from Sevilla, who occupy fourth spot after beating Real Betis 3-2 on Saturday.
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(Reporting by Richard Martin; Editing by Christian Radnedge)
