Marcelino Garcia Toral's men had previously looked capable of challenging for a UEFA Champions League place alongside Sevilla, Valencia and Atletico Madrid, but their season has been unravelling since losing to Unai Emery's side in the Europa League.
A 52nd-minute Ikechukwu Uche penalty gave Villarreal the lead, though the hosts hit back just after the hour mark, Diego Castro netting with a brilliant header.
Villarreal failed to retake the lead and ultimately settled for a draw, making it five matches without a win for Marcelino's side in La Liga, leaving them 11 points adrift of fifth-placed Sevilla.
Enzo Roco put Elche ahead just before the break and Chelsea-owned Mario Pasalic doubled their advantage in the 68th minute, with Borja Garcia's late red card compounding a miserable day for Cordoba, who sit nine points from safety.
Lucas Perez struck just before the break to cancel out Xabi Prieto's 33rd-minute penalty, but Chory Castro's stunning volley had seemingly sent the hosts on their way to all three points with a little over half-an-hour left.
The day's other game saw Espanyol beat Athletic Bilbao 1-0 at Cornella-El Prat thanks to Sergio Garcia's 40th-minute effort.
