The Brazilian's goal after just 10.5 seconds set the La Liga side on their way to a deserved victory and kept them in the hunt for the Round of 16 despite Stefan Kiessling's effort
Jonas opened the scoring for the hosts after 10.5 seconds, but Stefan Kiessling sent the sides into the break level with a header on the half-hour mark.
However, second-half goals from Roberto Soldado and Adil Rami secured the win for the Spanish side who are now just one point behind the second-placed Germans in Group E.
Valencia got off to the perfect start, capitalizing on an error by Bernd Leno in the Leverkusen goal to score right after kick-off as the young stopper cleared the ball straight into the path of Jonas, who pounced on the loose ball to send his side into the lead.
The goal, clocked after 10.5 seconds of play, was the second-fastest goal in Champions League history, narrowly behind Roy Makaay’s strike after 10.12 seconds for Bayern Munich against Real Madrid in the 2007 Round of 16.
Valencia dominated possession thereafter, however they were indebted to Diego Alves for preventing an equalizer in the 17th minute when the Brazilian made a spectacular diving save to deny Omer Toprak an easy finish at the back post following a corner.
The La Liga side were soon handed a blow in the 24th minute when Ever Banega had to be withdrawn due to injury and the Argentine midfielder, fighting back tears, was replaced by Tino Costa
Things went from bad to worse for Unai Emery’s men when Leverkusen evened the scoreline against the run of play on the half-hour mark.
Michael Ballack was released down the left flank and dinked in a clever cutback from the byline which Kiessling duly headed home from a few yards out.
Valencia were left ruing their inability to capitalize on their control of possession and the visitors smelled blood, ending the first-half on a strong note.
Alves had to be alert again in the 38th minute to tip over a stinging drive courtesy of Andre Schurrle from 20-yards out.
The German international went close again five minutes after the restart when he strode confidently into the area, but his effort from the right flashed wide of the far post.
Valencia managed to settle down shortly after and began to exert greater control over proceedings with some concerted spells of possession.
This time, they made their time on the ball count, taking the lead in the 65th minute through Soldado after Jeremy Mathieu broke free down the left and delivered a low cross into the path of the Spanish striker, just managing to get enough on the ball to take it past Leno.
The Mestalla was awakened, but they were almost silenced minutes later after Schurrle had a goal wrongfully disallowed for offside.
The German was clearly behind the last defender when he was put through on the right and finished past Alves, but the linesman’s flag halted the Leverkusen celebrations.
Valencia took advantage of their good fortune and scored their third goal 15 minutes from the end as Tino Costa’s corner was placed in the path of Rami, before outmuscling Lars Bender and nodding the ball past Leno to seal the points for the La Liga side.
Leverkusen were deflated after Rami's goal and spent the remainder of the match playing second fiddle to the hosts who stroked the ball around with relative ease behind their fans, who of course erupted with relief at the final whistle.
The result sees Valencia remain in third on five points, but they are now only one behind Leverkusen for second spot in Group E with two games remaining.
Chelsea remain on top in the group with eight points, while Genk prop up the table with two points.
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