Winners when the two met at Stadio Olimpico in Serie A less than a month ago, Atalanta thought more capital gains were on offer just eight minutes in, when a glancing Nikola Krstovic header found the net following a Davide Zappacosta cross, only to be ruled out by VAR for offside.
La Dea continued to take the aerial route, and four minutes on a curling free-kick from Lazar Samardzic was headed a whisker wide by Mario Pasalic.
That effort turned out to be the only official shot of the first 30 minutes, yet it took some last-ditch defending from Isak Hien to deny Daniel Maldini a golden chance as Lazio grew into the match.
But when the home side did finally have a shot, Gustav Isaksen saw his strike blocked by one of his own teammates.
Late in the half, Atalanta came within inches of the lead when Zappacosta struck a volley into the ground and bounced up past a stranded Ivan Provedel and onto the crossbar.
Whatever Maurizio Sarri said to his attackers at half-time, it had an immediate effect, as Lazio took the lead 63 seconds into the second half when Maldini slipped a perfect through pass to the onrushing Fisayo Dele-Bashiru, who coolly chipped the ball over the advancing Marco Carnesecchi.
However, the lead lasted all of four minutes, as Samardzic took aim from the edge of the box, and though Provedel managed to beat the effort away, he could only palm it to Pašalic, who gobbled up the rebound.
Kenneth Taylor was denied by Carnesecchi and Zappacosta saw a dipping effort clear the crossbar as the match entered the final quarter, and soon the chances dried up as both sides looked determined not to go into the second leg behind.
But with just three minutes to play, Lazio grabbed what they thought would be the winner in unorthodox fashion when a cross from the left was intercepted by Pasalic, who underhit his backpass to Carnesecchi, allowing Boulaye Dia to steal in.
Yet, for the second time, Atalanta hit back rapidly, and with 90 minutes on the clock, Kamaldeen Sulemana cut the ball back for Yunus Musah to hammer low past Provedel for 2-2.
It will be a winner-takes-all scenario when the pair meet in Bergamo for the second leg on 22nd April, as Raffaele Palladino’s side aim for a first Coppa title since 1963, while Lazio remain hopeful of lifting the trophy for a sixth time.
Flashscore Man of the Match: Fisayo Dele-Bashiru (Lazio)