Sanchez became Chile's all-time record scorer early on, passing Marcelo Salas with his 38th international goal after a mistake from Arsenal team-mate Shkodran Mustafi.
Eduardo Vargas hit the crossbar for Juan Antonio Pizzi's men, but Stindl struck for the second consecutive game before half-time.
A quieter second half did not produce a winning goal, meaning Chile and Germany stay level on four points at the top of Group B, three clear of Australia and Cameroon, who also drew 1-1 earlier on Thursday.
The two teams will progress to the last four if they avoid defeat in their final matches on Sunday, Chile facing Australia and Germany up against Cameroon.
Chile took the lead after only six minutes, Sanchez capitalising on Mustafi's misplaced pass to play a slick one-two with Arturo Vidal and stab a left-footed finish in off the near post from eight yards.
Stindl forced a sharp save from Johnny Herrera with a low strike at the other end, but it was Chile who came within inches of scoring the game's second goal.
Vargas seized on a loose ball 25 yards out and smashed a dipping strike against the underside of the bar, which bounced agonisingly to safety, having had Marc-Andre ter Stegen beaten.
Germany levelled four minutes before half-time when Emre Can's throughball found Jonas Hector, whose superb cross from the left allowed Stindl to slide in and convert from inside the six-yard box.
Sanchez worked space for himself and forced a one-handed save from Ter Stegen before the end of a first half which ended level.
The Arsenal star curled a free-kick just over after the break, while Vidal's looping header and Vargas' clever effort also narrowly missed the target.
Stindl's shot led to an unconvincing save from Herrera at the other end, but there was little late drama as Germany, who did not make any substitutions, extended their unbeaten streak to 12 matches.