Marcelino's side had the chance to close the gap on leaders Barcelona to two points with victory, but a late winner from Joan Jordan handed an improving Eibar team a surprise win after Santi Mina had earlier cancelled out Takashi Inui's opener.
The result lifts Eibar up six places to seventh, now only outside the top six on goal difference having extended their unbeaten streak to five games.
Valencia, meanwhile, are condemned to just their second defeat of the season and could see the gap to Barcelona grow to eight points should the league leaders beat Deportivo La Coruna on Sunday.
Clear chances were few and far between during a tight and largely uneventful first half, with neither side creating a notable opportunity until Mina drove an effort narrowly past the post from the edge of the box in the 37th minute.
It was a different story in the second half, though, as Inui broke the deadlock just four minutes after the restart when he beat Neto from the edge of the box having collected the loose ball from a rebound.
Eibar's lead lasted only eight minutes before Valencia restored parity shortly before the hour mark, with Mina finding space inside the box to turn Andreas Pereira's cross past the keeper.
It looked as though the contest would be heading for a draw until Eibar restored their advantage three minutes before the end of normal time when Jordan rose highest to power his header in from a difficult angle and gift the hosts all three points.
Eibar have now won four of their last five La Liga games having won just one of their 10 prior to that, whereas Valencia were unbeaten until the start of the month but have now lost two of their three outings in December.
Eibar (4-4-2): Dmitrovic; Capa, Oliveira, Arbilla, Angel; Ivi (Pena, 93'), Jordan, Garcia, Inui; Charles (Kike, 72'), Enrich (Escalante, 85')
Valencia (4-4-2): Neto; Montoya, Gabriel, Vezo, Gaya (Lato, 46'); Pereira (Torres, 81'), Parejo, Kondogbia, Gil (Guedes, (73'); Rodrigo, Mina