Jonas pounced on a defensive error to grab his lightning-quick goal but the Germans recovered their composure and Stefan Kiessling headed them level in the 31st minute.
Roberto Soldado put Valencia back on course for their first group win this season, flicking in a Jeremy Mathieu cross in the 65th minute, and Adil Rami nodded the third at a corner in the 75th.
Valencia have five points from four matches, one behind Leverkusen and three adrift of leaders Chelsea who drew 1-1 at bottom club Racing Genk (two points).
"We started really pumped up and the quick goal was phenomenal for us," Soldado told Spanish television.
"We knew these next three games were all finals. We have won the first, next we need to beat Genk at home and then we need to go to London knowing that by then a point could be enough."
From the opening kick-off Leverkusen passed the ball all the way back to keeper Bernd Leno but he scuffed his low clearance straight to Jonas and the striker tucked his shot just inside the post.
The effort was just two seconds short of the quickest Champions League goal scored by Dutchman Roy Makaay for Bayern Munich against Real Madrid in 2007.
Valencia had their tails up until playmaker Ever Banega was forced off with a knee injury in the 24th minute and the Germans rallied.
Michael Ballack, playing with a face mask to protect a broken nose, crossed for Kiessling to nod the equaliser as Diego Alves was proving the busier of the two keepers.
Valencia regained the lead though when Spain striker Soldado flicked a shot past Leno with the outside of his boot and France defender Rami made sure of the points.
"That early goal played a key role tonight," said Leverkusen coach Robin Dutt.
"The team was a bit stunned but they showed a good reaction and scored a great goal. In the second half we played a bit too riskily and we were punished for it."
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