German Denis gave the Bergamese club the lead in the fourth minute and Federico Peluso made it two in the 38th minute.
Amauri brought Parma back into the game on the stroke of half-time but, despite their efforts, they were unable to find an equaliser in the second half.
The win lifts Atalanta nine points clear of the relegation zone and above their opponents into eighth place.
The game opened with a quickfire goal for the home side as Denis headed in Ezequiel Schelotto's cross, with Parma goalkeeper Antonio Mirante left standing.
Only four minutes were on the clock, leaving Parma with plenty of time to respond, but there was plenty time for Atalanta to build up a more convincing lead, which seemed the more likely outcome in the opening exchanges.
Stefano Colantuono's Nerazzurri continued to pose the greater threat with Peluso's excursions down the left causing persistent problems.
Unsurprisingly, the hosts doubled their lead in the 38th minute when Denis' shot was only parried by Mirante to Peluso, who crowned another of his surges forward with the second goal.
Atalanta then committed the cardinal sin of taking their foot off the accelerator to allow Parma to reduce the arrears on the stroke of half-time.
Amauri popped up inside the penalty area to head in a goal which would have changed both Colantuono's and Roberto Donadoni's respective half-time team talks.
Donadoni probably told his players to keep at it, which they did.
Amauri and Nicola Sansone both went close with Gabriel Paletta missing Parma's best chance in the 67th minute, sending a free header wide of the post.
Atalanta could have won by a greater margin in the end but Giuseppe De Luca wasted a chance with only Nicola Pavarini - who replaced the injured Mirante - to beat in the fourth of five minutes of stoppage time.