Atalanta had won 11 of its last 13 league games — drawing the other two — and beat Brescia 6-2 midweek but it struggled to break Verona down.
Atalanta eventually broke the deadlock five minutes into the second half when Koray Günter lost the ball and Zapata rushed in, used his strength to hold off the Verona defender, and fired into the bottom corner.
It was Zapata’s third goal in as many matches.
But Verona was back on level terms shortly after when Atalanta goalkeeper Pierluigi Gollini could only parry Amir Rrahmani’s strike and Pessina fired in the rebound.
Mario Pašalić almost won it for Atalanta in stoppage time but volleyed a cross inches wide of the left post.
GOALLESS STREAK ENDED
Sassuolo dominated but could only manage a 1-1 draw at 10-man Cagliari, which scored for the first time in five matches.
The visitors created plenty of chances but put only one of them away when Francesco Caputo was left unmarked to head in at the back post after a corner was deflected toward him in the 12th minute.