The Socceroos midfielder netted the opener against FC Carl Zeiss Jena 30 minutes into the German sides' Thuringer Medien Cup clash in Jena on Sunday.
Leckie clinically finished some good link-up play across midfield by Julius Kade and Maurice Covic, running onto a through-ball and finding the net with a first-touch shot just inside the 18-yard box.
Hertha Berlin, who finished fifth in the Bundesliga last season to qualify for the Europa League, doubled their advantage when Alexander Esswein slotted home a penalty.
Leckie, 26, signed for Hertha Berlin in May after his former club Ingolstadt was relegated from the German top flight.
Leckie's Socceroos teammate Jamie Maclaren also found the net during his debut for 2.Bundesliga side Darmstadt 98.
Darmstadt were involved in two matches over a busy weekend, defeating SV Wallern 4-3, while also accounting for Turkish club Rizespor 2-1.