Lucas Alcaraz's men looked set to go down to a 14th league defeat of the season when midfielder Saul Berjon's volley put Eibar ahead in the 55th minute.
But Levante responded superbly and levelled matters just 10 minutes later through David Barral's clever close-range finish from Tono's ball into the box.
And Kalu Uche completed the turnaround in the 67th minute, the Nigerian capitalising on some dreadful defending from Eibar to slot home at the near post.
Dani Garcia then saw red for Eibar a minute from time for a second bookable offence.
The win puts Levante a point clear of the drop zone in 16th, while Eibar's seventh straight loss leaves them two points better off in 13th.
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