Goals from Giovanni Fabbian and Simone Lontani, alongside a Davide Zappacosta own goal, gave Alberto Gilardino his first victory as Parma manager.
Atalanta started brightly and appeared to have taken the lead through Nikola Krstović in the eighth minute, but the goal was ruled out for offside following a VAR check.
Charles De Ketelaere also threatened on several occasions, while Ederson came close with a long-range effort. However, the hosts failed to convert their early dominance into goals.
Parma punished them shortly before half-time when Vincent Sierro delivered a corner into the penalty area and Giovanni Fabbian rose highest to head past Marco Carnesecchi in the 41st minute.
The visitors went into the break with a 1-0 advantage, despite Atalanta creating several opportunities.
Parma punish Atalanta after the break
The second half began disastrously for the hosts as they conceded another goal just two minutes after the restart.
El Bilal Touré delivered a dangerous cross from the right, and Zappacosta inadvertently diverted the ball into his own net while attempting to prevent Lontani from reaching it.
Parma extended their advantage in the 58th minute when Fabbian turned provider, setting up Simone Lontani to produce an excellent right-footed finish from outside the penalty area.
Atalanta attempted to respond, with substitute Kamaldeen Sulemana and Nikola Krstović testing Parma goalkeeper Giovanni Daffara.
Mario Pašalić also came close to reducing the deficit, but his close-range header struck the crossbar as Parma continued to defend resolutely.
Daffara produced further important saves in the closing stages to preserve his clean sheet and complete an outstanding performance.
Parma climb out of the relegation zone
The victory moved Parma to eight points from their opening 10 league matches, lifting them out of the relegation zone and level on points with Fiorentina and Sassuolo.
It was also Gilardino's first victory since taking charge of the club, offering encouragement after a difficult start to his tenure.
Atalanta, meanwhile, remained on 11 points and 13th in the standings following their fifth defeat in 10 league matches.
Maurizio Sarri's side have now gone five matches without a victory across all competitions, increasing the pressure to improve their performances.
Parma will look to build on the result when they host Bologna on Saturday, while Atalanta turn their attention to their next European assignment.
Final score: Atalanta 0-3 Parma
Goalscorers:
• Parma: Giovanni Fabbian 41', Davide Zappacosta 47' (og), Simone Lontani 58'.
Man of the Match: Giovanni Daffara (Parma)