Gian Piero Gasperini's side are closing in on a third consecutive season of Champions League football as they sit two points ahead of third-placed Napoli with three games to play.
Juventus and AC Milan are a further point behind the Bergamo side before they clash later on Sunday in Turin. Ruslan Malinovskyi put Atalanta ahead in the 12th minute.
Muriel and Matteo Pessina came on after the break and the Colombian set up the Italian for the second six minutes later. Muriel then struck twice within 10 minutes in the final quarter of an hour to bring his tally to 21 goals this campaign. Aleksei Miranchuk grabbed a fifth in injury time after Juan Brunetta and Simon Sohm had pulled two goals back late for Parma.
Earlier Sassuolo kept their Europa League hopes alive with a 2-1 win over Genoa, with goals in either half from Giacomo Raspadori and Domenico Berardi. Roberto De Zerbi's side are seventh, one point ahead of Roma who host relegated Crotone later on Sunday.
Cagliari won the battle with relegation rivals Benevento 3-1, to move four points clear of the relegation zone.
Standout matches today