Lars Stindl scored in the 20th minute after Chile midfielder Marcelo Diaz gave the ball away on the edge of his penalty area.
Chile, playing with their trademark high-octane style and driven forward by another relentless display by Arturo Vidal, dominated the match but finished poorly.
There was a controversial incident involving video technology in the second half when Chile defender Gonzalo Jara elbowed Timo Werner by the touchline.
Serbian referee Milorad Mazic initially missed the incident, was alerted to it, then let Jara off with a yellow card instead of a red.
There was late drama deep in stoppage time when Germany goalkeeper Marc-Andre ter Stegen dived to push away an Alexis Sanchez free kick.
The win could be a bad omen for Germany, however, as no team has ever won the World Cup after lifting the Confederations Cup the year before.