Josip Ilicic scored all of Atalanta's goals in a 4-3 win at the Mestalla which had been closed to fans due to fears over the spread of the coronavirus.
Leading 4-1 from the first leg in Italy, Atalanta were a goal to the good within five minutes after Ilicic converted a penalty.
Kevin Gameiro levelled for Valencia in the 21st minute and evened matters again early in the second half after Ilicic's second goal.
Valencia then took a 3-2 lead before Ilicic ended any hopes of a revival to become the first man to score four times away from home in a Champions League knockout match.
Return
It completed a fairy-tale comeback for Atalanta who lost their first three games in the group stages.
"After a difficult start to this competition, we got the hang of it," said Atalanta coach Gian Piero Gasperini.
The match was played without fans as European football associations respond to the threat posed by the Covid-19 virus.
Atalanta are based in Bergamo, one of the regions in Italy worst affected by the disease which has left more than 600 people dead in the country.
After the final whistle, the Atalanta players held up a shirt emblazoned with the message: "Bergamo, this is for you!"
"We are very happy with how we have represented a region that suffers so much," said Gasperini.
On Wednesday night, Paris Saint-Germain's second leg tie against Borussia Dortmund will be played at the Parc des Princes in Paris without fans.
However Liverpool's second leg match against Atletico Madrid will take place at Anfield with supporters present even though the number of coronavirus infections is rising in Britain.
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