The Portuguese started the first of a final six races in the space of nine days in the German capital from pole position with DS Techeetah team mate Jean-Eric Vergne, the defending champion, alongside.
He then led from start to finish and also set the fastest lap to become the first double winner this season.
"Everyone is assuming that I have to win it and that is a lot of pressure but I take it well," he said of his status as title favourite.
Yes I want to win it, but there is a long way to go.
Da Costa had also won the last race before the season was suspended in March and now has 96 points to New Zealander Mitch Evans' 56 for Jaguar.
Vergne's race fell apart with minutes to go while he was running second, the Frenchman dropping down the order and having to pit after contact with Audi's Brazilian Lucas di Grassi.
Germany's Andre Lotterer finished runner-up for Porsche, 5.5 seconds behind, and Envision Virgin Racing's British driver Sam Bird completing the podium from seventh on the grid.
The next race is on Thursday.