Atalanta responded with an equalizer from Francesco Gasparello's header, but Derry scored again before halftime to put Chelsea back in the lead.
In the second half, Genesis Antwi found Walsh with a pass, and he finished the play to secure a 3-1 win for Chelsea.
Chelsea made a late substitution, bringing on Matias Eboue, who is the son of former Arsenal player Emmanuel Eboue.
