Hans Hateboer's first two goals of the season, paired with stunning efforts from Josip Ilicic and Remo Freuler, gave La Dea a cushy aggregate advantage ahead of the return leg in Spain on March 10.
Mario Pasalic nearly handed the hosts an eighth-minute lead when his one-two with Ilicic resulted in an effort that Jaume Domenech narrowly pushed above the bar.
But the frenetic matchup was never going to end in a goalless stalemate.
Right-sided wing-back Hateboer made a darting far-post run that the evening's standout player, Alejandro Gomez, found with a low cross. Ilicic doubled the scoreline moments before the break when the Slovenian striker beat Domenech with an off-foot rocket on his rarely used right peg.
Up two goals at the interval, manager Gian Piero Gasperini's commitment to attacking football didn't waver. His charges came out of the break and continued pushing forward, often affording their opponent opportunities to forge their own threatening endeavors.
Freuler produced the night's best finish a dozen minutes after the half - a thrilling, curling effort past the reach of Domenech - before Hateboer added a fourth goal with a low shot into the far corner.
Eventually, Atalanta were stung for their aggressive approach, conceding a 66th-minute marker on substitute Denis Cheryshev's first touch of the match.
Gasperini and Co. will circle March 10 on their calendars for the reverse leg at Valencia's Mestalla Stadium.
Estimates suggest Atalanta sent 40,000 supporters to the home ground of AC Milan and Inter for Wednesday's meeting after their own Bergamo digs were ruled insufficient by UEFA standards.
In their first-ever European appearance, Atalanta are now one step from the last eight after becoming the first club to progress to the knockout round with losses in its opening three group-stage fixtures.