Hans Hateboer was the star of the first leg show with a goal in each half.
Josip Ilicic and Remo Freuler were also on the scoresheet for the hosts who had to play at AC and Inter's stadium in Milan as their own ground 55km away in Bergamot fails to meet the standards for European games.
Such logistics and technicalities were the least of the partisans' worries for the club's first foray into the knockout stages of European club football's most prestigious competition.
Blitz
Hateboer opened the scoring after 16 minutes when he stabbed Alejandro Gomez's cross past the Valencia goalkeeper Jaume Domenech.
Three minutes before the pause, Ilicic doubled the advantage with a powerful strike into the top corner.
Freuler and Hateboer added to the tally before the Russia international Denis Cheryshev pulled one back for the visitors.
"This is an evening that we'll remember forever," said Atalanta coach Gian Piero Gasperini after the match. "It's an amazing result, full of emotion."
Recovery
An Atalanta berth in the quarter-finals appeared an ocean away after the first three games of the group stages. Gasperini's men had shipped 11 goals in losses to Dinamo Zagreb, Shakhtar Donetsk and Manchester City.
Their fortunes turned on 6 November when they held Manchester City to a 1-1 draw at the San Siro.
Victories over Dinamo and Shakhtar eventually pushed them up into second behind City.
"Three goals ahead is a nice reward," added Gasperini. "But there were a lot of dangerous situations for Valencia and these are things we'll need to improve in Valencia.
Assets
"But we are satisfied with this victory and above all with this advantage. Before the match day I would have signed up to go to Valencia in the return game with a three-goal lead."
Valencia will be bolstered for the return leg on 10 March at the Mestalla by the return of several key players who missed the first leg due to injury or suspension.
"It's a pretty overwhelming result, this 4-1," said Valencia coach Albert Celades. "It certainly complicates things a bit.
"We had opportunities and we didn't finish them. This result is clear enough but it's not impossible to turn things around. Let's see what happens at Mestalla, let's play well in our stadium."
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