Unai Emery's side couldn't answer Malaga's victory with another let down defensively in a disappointing display and now only four points separate the clubs for third place
Los Che, who entered the day only three points above Malaga in the race for third place, managed to convert twice during a dominating spell, only to see Emilio Nsue and Victor level the game in an eight-minute span early in the second half.
In similar fashion to the events that took place at the stadium on Thursday against PSV in Europa League round of 16 action, poor goals were surrendered after letting their guard down.
Early on in the match Valencia were in fine form; pressure from the hosts saw Joaquin Caparros' men struggle to string passes together.
With the visiting attack having nothing to do thanks to constant possession, Unai Emery's men had chance after chance to go ahead early.
A ball from Costa into the box found Roberto Soldado open eight minutes in, but the Spain international's bullet shot was saved well by Dudu Aouate.
After a few more close calls, Costa put his side up 1-0 after 23 minutes with a shot from the top of the box that deflected off a diving Jose Nunes, before flying over the goalkeeper and into the net.
With the lead, the home side doubled the score three minutes from the break after a costly error from the visitors. Nunes passed a soft ball back to Aouate, but the Israeli custodian tried to cut away from the oncoming Soldado with a touch, only to see Aduriz steal the ball from 12 yards out and finish into the open net.
In the second half, life was injected into the contest with a goal by Mallorca. Michael Pereira delivered a perfect through ball into the box that split the Valencia defence, allowing Nsue to finish low past Vicente Guaita in the 57th minute.
Eight minutes later, the visitors levelled the score via Victor, who struck home a cross from Nsue at the back post with a little poke after Jeremy Mathieu was caught watching.
With the game hanging in the balance, Costa received a red card for a tough challenge on Alejandro Alfaro six minutes from time, as neither team could find the winning goal as time expired as the hosts earned a tough draw to move into 14th place in the league.
Next up, Los Che will travel to face PSV on Thursday in the second leg of the cup tie, holding a 4-2 advantage. Mallorca will return to the pitch on Sunday when they host Atletico Madrid in league play.