The France striker was on hand to tuck home an early chance, a predator's goal, and his late penalty sealed a 3-1 aggregate triumph, raising the possibility of Leipzig lifting a first European trophy in its history.
Head coach Domenico Tedesco has transformed Leipzig's fortunes since replacing Jesse Marsch in December and the German visitor had too much for their Italian host here.
After seven goals in the UEFA Champions League this season, Nkunku now has three in this competition. Two years after a UEFA Champions League semi-final defeat to Paris Saint-Germain, the German outfit is back at the business end of a European campaign.
Atalanta's Davide Zappacosta drew a decent early save from Leipzig captain Peter Gulacsi, who got down well to block a low shot at his near post.
Leipzig then took the all-important 18th-minute lead when Konrad Laimer was allowed to run 50 yards unchallenged along the right flank and into the Atalanta penalty area, before cutting back for Nkunku to smash in off the right post from close range.
Dani Olmo had a chip comfortably caught by Juan Musso as Leipzig sought a second goal, while at the other end a low shot from Jeremie Boga was blocked.
Atalanta wanted a penalty early in the second half when Ruslan Malinovskiy's powerful free-kick hit Olmo on the arm, and it looked a credible shout, yet the hosts were denied after a VAR (video assistannt referee) review.
Laimer almost added a second for Leipzig when a rapid counter-attack ended with Musso seemingly making a mess of reading his defenders' intentions, having to scramble to keep the lead down to one goal.
Nkunku was sharp for Leipzig and wriggled through to create a chance for himself as Musso blocked at the cost of a corner. As Atalanta became increasingly desperate, a foul by Musso on Nkunku gave the striker a chance to finish the tie, which he took by firing high into the left corner.