The La Liga outfit recorded a comfortable victory over Tony Pulis' side to progress to the last 16 of the competition, with Jones wasting the Premier League team's best chance
An uneventful encounter saw the home side take the lead early on through Jonas from close-range. The visitors offered little in response, with Kenwyne Jones missing their best chance when one on one.
The home side made eight changes to the side that was humbled at Camp Nou on Sunday. Adil Rami, Jonas and Pablo Piatti were the only players to retain their place in the starting XI, with Roberto Soldado not even making the bench.
Likewise, the visitors made nine changes to the side that progressed to the quarter-finals of the FA Cup against Crawley Town at the weekend, with Dean Whitehead and Rory Delap the only survivors.
Jones and Ricardo Fuller partnered Cameron Jerome in a three-pronged attack, while Tony Pulis named just four substitutes.
The home side almost doubled their aggregate lead within 90 seconds of the kick-off.
After Piatti had been brought down on the edge of the Stoke area by Salif Diao, Dani Parejo rattled the resulting free-kick back off the crossbar with Thomas Sorensen well-beaten.
With 20 minutes gone the visitors missed a golden opportunity to level the tie.
Wilson Palacios picked up the ball in midfield and threaded a perfectly weighted ball through to Jones. The big forward composed himself before lashing his left footed effort across goal, only for Valencia goalkeeper Vicente Guaita to tip the ball wide.
Shortly after, Tony Pulis’ men paid the price for squandering their big chance.
After Pablo Hernandez had shown Danny Collins a clean pair of heals down the Stoke left, the Spain international reached the byeline before cutting the ball back to the unmarked Jonas, who was left with the simple task of giving his side the lead and leaving Stoke with a mountain to climb.
Now needing to win by two clear goals to progress, the visitors wasted no time in picking themselves back up, with Jones stinging the fingertips of Guaita with a well-controlled half-volley, following an intelligent knock down from Jerome.
With the game beginning to slip away from the Potters and Valencia looking comfortable, Stoke began to pour forward in attack, but their cavalier approach nearly cost them as it was the home side who almost had the last word of the half.
Following a superb lofted ball from Mehmet Topal, Bruno found himself with room in the box but his cut back was scuffed by Aritz Arduiz and Stoke clawed their way through to half time.
After a slow start to the second period, Pulis opted to roll the dice and looked to the bench. However, with no Peter Crouch or Jonathan Walters and only three outfield players to choose from, his options were limited.
Jermaine Pennant and Ryan Shotton entered the fray, but still it was the home side who looked the more threatening.
Following a clumsy challenge from Robert Huth, Parejo was handed another opportunity from a dead-ball situation. The young Spaniard did well to get the ball up and over the wall but was denied by a fine save from Sorensen.
Yet more clumsy defending from Stoke, this time Jonathan Woodgate the culprit, handed Valencia another great chance.
Hernandez stepped up to take responsibility, but his effort flew agonisingly over the crossbar with Sorensen rooted to the spot.
Valencia sail through to the last 16 of the competition, 2-0 on aggregate, as Stoke now look to focus on their domestic campaign.