The victory, from ninth on the grid at the circuit around the city's old Tempelhof airport, was Evans' second in a row - after Sao Paulo on March 25th - in the all-electric world championship.
"It’s an incredible feeling to get back-to-back wins, particularly in Formula E where it’s so challenging," said Evans.
"I needed a couple of good races and this is exactly what the team delivered today in Berlin. There is still a long way to go this season but the main thing is we’re back in the hunt."
Maximilian Gunther (25) finished third for Maserati for his first points of the season, with polesitter Sebastien Buemi (34) fourth for Envision.
Porsche's Pascal Wehrlein (28) retained the overall lead after starting 15th but finishing sixth in a race that had eight different leaders from start to finish.
The German now has 94 points after seven rounds of the season to lead Envision Racing's Nick Cassidy (28), who finished fifth in the race, on 71 and DS Penske's Jean-Eric Vergne (32) on 66. Evans moved up to fourth on 64.
Berlin hosts a second race, round eight, at the same venue on Sunday.
