Roberto Soldado scored twice, the second a penalty, after Victor Ruiz's opener as the hosts stunned PSV with three first-half goals.
The Dutch side looked down and out when Pablo Piatti added a fourth - the 10th goal PSV have conceded in five days following their 6-2 Eredivisie defeat by FC Twente on Sunday - but an Ola Toivonen penalty in the 83rd minute and another goal from Georgino Wijnaldum in the 90th minute got them back in the tie.
Valencia came flying out of the blocks and were two up after 13 minutes.
Pablo Hernandez jinked into the area following a short corner and crossed to the back post where Victor Ruiz rose highest to head home the opener after 11 minutes.
The visitors were cut open again two minutes later as Antonio Barragan drove inside from the right and laid the ball across the area for Soldado to slide home.
Jonas then could not adjust his feet quick enough to turn home a corner from Daniel Parejo after the ball had come all the way through to him at the back post.
The hosts were in total control, but PSV might have pulled one back when Tim Matavz got to Stanislav Manolev's cross ahead of goalkeeper Diego Alves but stabbed his effort wide of the near post.
That was a rare moment of promise for the Dutch side, though, and Valencia should have had a third when Piatti was presented with a free header in front of goal by Barragan's right-wing cross.
He could only direct his header straight at goalkeeper Andreas Isaksson, who made the save.
Los Che did made it three in the 43rd minute when Jonas went down in the area under a challenge from Kevin Strootman and Soldado sent Isaksson the wrong way from the spot.
And PSV's hopes looked in tatters 11 minutes after the break as Piatti got a fourth, the striker running on to a pass from Parejo and sliding his finish past Isaksson.
The visitors were not even looking like getting a consolation and they almost conceded another when Jonas' free-kick brought a sprawling save from Isaksson.
But suddenly PSV were offered a way back into the tie when Jeremy Mathieu needlessly went to ground in the area, bringing down Strootman, and Toivonen made no mistake from the spot.
And substitute Wijnaldum tucked home another from close range in the dying moments to put a different complexion on the tie.