Sanchez capitalised on a mistake by Gunners team-mate Shkodran Mustafi to open the scoring.
Lars Stindl stabbed in an equaliser for Germany just before the break.
The result means Chile remain top of Group B, ahead of Germany on goal difference.
“I’m very happy to be Chile’s top scorer. Our dream is to win this tournament and we feel we have a chance,” said Sanchez, who has been linked with a move away from Arsenal this summer.
“We played well in the first half, but Germany adapted very well to how we were playing.”
Chile and Germany need just one point from their remaining Group B games against Australia and Cameroon respectively to progress to the semi-finals.
Earlier on Thursday, a Mark Milligan penalty cancelled out an Andre-Frank Zambo Anguissa goal as Australia and Cameroon drew 1-1.