After Martin Hinteregger gave Augsburg an early lead, Leckie pulled one back for the German capital side on 28 minutes with a crisp finish following a cushioned pass from Davie Selke.
Hertha then managed to take the lead three minutes later through Duda but couldn't hold on for the victory as Koo Ja-Cheol earned a draw for Augsburg.
The result means Hertha sit in seventh place on the Bundesliga table, four points out of the Champions League qualification places.
Leckie's return to form will be a welcome sight for Socceroos coach Graham Arnold as he prepares the national team for their defence of the Asian Cup next month.
The 27-year-old attacker is expected to play a vital role in an Australian team that is searching for goals since the retirement of talisman Tim Cahill.