Atalanta move level on points with second-placed Inter Milan, but are six points adrift of Serie A leaders Juventus.
On-loan Pessina headed in just before the hour mark in Verona minutes after Colombian striker Duvan Zapata had put the visitors ahead. Atalanta are equal on 71 points with Inter Milan, who travel to fifth-placed Roma on Sunday, with eight-time reigning champions Juventus, hosting fourth-placed Lazio, who are eight points adrift of top spot, on Monday.
Atalanta have scored in a club record 22 games in a row, but Zapata's second-half goal was not enough to bring home the three points. Gasperini's side are the only team to remain unbeaten on the road this season, but their hopes of a first Scudetto in the team's 112-year history are all but over with four games left to play.
"Talking about the Scudetto is too much. We lack a point to get to the Champions League," said Gasperini. "Ours was a good match against a team that is doing well and wanted to recoup after a controversial defeat against Roma."
Verona, in ninth, are coached by ex-Croatia midfielder Ivan Juric, who played under Gasperini in Genoa and was his assistant at Inter Milan and then Palermo. Atalanta threatened early with Mario Pasalic, scorer of a hat-trick against Brescia this week, forcing a save from Marco Silvestri after quarter of an hour.
Zapata came close before the break, before getting his chance five minutes into the second half pouncing on a Koray Gunter defending blunder to blast past Silvestri. Zapata pulled Atalanta ahead after the break with his 18th goal in all competitions this season. But four minutes later midfielder Pessina drew Verona level, sending in a rebound for his seventh league goal this season, after Gollini denied Amir Rrahmani.
AC Milan host Bologna later on Saturday looking to move into the Europa League places with in-form Sassuolo travelling to Cagliari.