The hosts, who had found the net just twice in their opening four games, made amends in an explosive game which saw six goals scored before half-time.
Atalanta's Giacomo Bonaventura cancelled out Djamel Mesbah's opener in the 20th minute. Two goals from Marco Parolo and one from Aleandro Rosi handed Parma a 4-1 lead with 10 minutes to go in the half, but German Denis reduced the arrears before the break.
Parma striker Carvalho Amauri was sent off for dissent early in the second half and although Atalanta substitute Marko Livaja cut the deficit 4-3 with 11 minutes remaining, the Gialloblu held on for victory.
The result eased the pressure on Parma coach Roberto Donadoni but piled further misery on Atalanta, who have lost four of their opening five games.
Parma enjoyed a strong start and went ahead in the 19th minute when Mesbah's bullet strike from outside the area beat Atalanta goalkeeper Andrea Consigli.
Atalanta drew level seconds later when Denis spotted Bonaventura in the box and his right-footed effort beat Parma goalkeeper Antonio Mirante.
Parma went back in front thanks to Parolo's powerful left-footed volley that beat Consigli.
In the 35th minute, Rosi got behind Marco Marchionni's pass and he struck a right-footed shot from outside the area that went into the bottom right corner.
Parolo scored his second of the evening five minutes later.
Antonio Cassano's attempt rebounded off the crossbar and Parolo was quick to react and slot in his team's fourth.
A fast break by Atalanta saw Bonaventura serve Denis in the box and he struck the ball past Mirante.
Parma continued to press forward after the re-start but were hindered when the referee showed a straight red card to Amauri. He was punished for complaining to an official after failing to receive a foul in a contrast with Mario Yepes.
Although Parma defended deeply, Atalanta had some chances to reduce the deficit and they did as Livaja's header from Luca Cigarini's cross beat Mirante.