The Polish goalkeeper had an outstanding match as he kept the hosts at bay with at least half a dozen top-quality saves.
Hans Hateboer wasted Atalanta's best chance when he contrived to head over from point-blank range from Josip Ilicic's assist after nine minutes.
After that, Atalanta laid siege to the Empoli goal but a combination of poor finishing, free kicks into the wall, heroic defending by the visitors and Dragowski prevented them from scoring.
The draw left Atalanta sixth in Serie A with 53 points, two behind fourth-placed AC Milan and one behind Roma. The top four qualify for the Champions League next season.
Empoli, 18th in the 20-team table, stayed in the relegation zone but are only two points behind Bologna, the team immediately above them.
(Writing by Brian Homewood; Editing by Toby Davis)
