A long-range blast from Marten De Roon near the hour mark put Atalanta ahead again. Muriel then tapped in a perfect cross from Chiesa to finish off a counterattack in the 79th.
Atalanta nearly won it in stoppage time with a header from Hans Hateboer that hit the bar.
Atalanta won the Italian Cup in 1963 for its only title while Fiorentina last claimed the trophy in 2001.
Lazio and AC Milan drew 0-0 in the first leg of the other semifinal on Tuesday.
Return legs are scheduled for April 24, with the final May 15.