Duvan Zapata bagged a second-half brace as Atalanta came from two goals down to hold Ajax 2-2 in their first Champions League game played in their home stadium in Bergamo on Tuesday.
Atalanta's European matches last season were all played at Milan's San Siro while their home ground was being upgraded to meet UEFA regulations.
The hosts, however, got off to a sluggish start on their return to the Gewiss Stadium in a game played behind closed doors in northern Italy because of the coronavirus crisis.
Ajax were two goals up at the break thanks to Atalanta's blunders with Dusan Tadic slotting in a penalty and Lassina Traore making the most of a goalkeeping error.
Gian Piero Gasperini's side had won their opener 4-0 at Danish club Midtjylland with Ajax losing 1-0 at home against Liverpool.
Atalanta are second in Group D, two points behind Livepool who beat Midtjylland 2-0, with the top two teams playing in Bergamo on November 3.
Ajax are third with one point.
Josip Ilicic missed chances to break through early as he returned to European competition for Atalanta, having missed over three months of action because of personal problems.
The Slovenian set up Zapata, but the Colombian wastefully sent wide before Robin Gosens caught Traore with a high boot, prompting the referee to point to the spot.
Tadic made no mistake against Marco Sportiello in the Bergamo goal.
And it was a Sportiello error which allowed the Dutch outfit to add a second eight minutes later as he fumbled a David Neres cross, with forward Traore on hand to finish off.
After the break Gasperini's side pushed forward, with Zapata reducing the deficit nine minutes later when he rose brilliantly to nod in a Papu Gomez cross.
The Colombian added a second on the hour, picking up a Mario Pasalic cross to burst into the area and finish off for his third European goal this season.