Valencia were held to a 2-2 draw at Racing Santander while Real Sociedad thumped Sporting Gijon 5-1 in La Liga on Sunday.
Unai Emery's side are third on the table and they were favourites against a struggling Racing side.
But Valencia were behind as early as the second minute as Adrian opened the scoring for the hosts.
A pair of strikes from substitute Aduriz on 66 and 80 minutes looked to have given Valencia the win, only for late drama to follow.
Firstly, Bernardo equalised with two minutes to play before Racing's Munitis and Valencia's Ricardo Costa were both given straight red cards in stoppage time.
The fiery contest saw no less than 10 yellow cards handed out in addition to the two sending-offs as referee Alfonso Alvarez Izquierdo was kept on his toes.
Real Sociedad made the perfect start in their easy win with David Zurutuza scoring twice inside the opening three minutes.
The midfielder was forced off the pitch after just five minutes following a head clash with Sporting's Gregory Arnolin, with the club confirming after the match that he had broken his nose.
But the damage appeared to be done, and although Sporting mustered a goal through Miguel de las Cuevas, Gorka Elustondo, Mikel Aranburu and Antoine Griezmann all netted second-half strikes for the winners.
In other matches, a 10-man Getafe won 2-1 at fourth-placed Levante while Granada won by the same scoreline at Real Betis.