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The visitors almost broke the deadlock after half an hour when Gomez's strike hit the bar.
Three minutes after half time, Gomez gave Atalanta the lead, squeezing the ball in from a tight angle.
Alberto Paloschi could have equalised immediately, but his strike was kept out by Sportiello.
Chievo continued to pepper the Atalanta goal, and Riccardo Meggiorini went close just after the hour mark.
With minutes remaining, Pellissier equalised from close range following a corner to grab a point for the home side.