Pablo Sarabia's 55th-minute strike appeared to have sent the Andalusians above champions Barcelona, who face Espanyol later, but the draw took them second on 28 points, level with the leaders and third-placed Atletico Madrid.
A dull first half gave way to an exciting second with Tomas Vaclik making a good save to deny Valencia midfielder Carlos Soler.
Sarabia broke the deadlock with his fifth league goal of the season when he pounced to score from close range, after Wissam Ben Yedder's effort was deflected into his path.
Ever Banega and Andre Silva hit the woodwork for Sevilla as they tried to stretch the lead but poor finishing meant Diakhaby was able to rescue a point for Valencia at the death as Vaclik misjudged Dani Parejo's free kick.
Despite their equaliser, Valencia fans whistled their team at the end of the game, disappointed with their ninth draw of the season which left them 12th in the standings.
(Reporting by Rik Sharma, editing by Ed Osmond)
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