Low may be pleased that Gotze's 16th-minute effort gave his side an impressive scalp as they build towards this summer's World Cup, but Chile proved they will be no pushovers in Brazil.
Germany goalkeeper Manuel Neuer had to make a couple of timely saves and on the one occasion he was beaten, Eduardo Vargas saw his strike cannon off the crossbar.
In the end, the home side held out and will still be regarded as one of the favourites for glory in Brazil - although boss Low may still need some convincing.
In the build-up to Wednesday night's clash, the Germany boss insisted he was not satisfied with the current form and condition of his players with less than 100 days to go before the World Cup gets under way.
They were given an early test of their credentials when Marcell Jansen had to block Arturo Vidal's header before going up the other end and scoring from their first attack.
It was the under-fire Mesut Ozil, who has been criticised this week as a result of his poor recent performances for Arsenal, who provided the telling pass into the area for Gotze to blast into the top corner.
Yet, the South American side nearly brought themselves level only for Neuer to make a fine save from Juventus' former Bayer Leverkusen midfielder Vidal's header, while Felipe Gutierrez's free-kick from just outside the area sailed wide.
At the other end, Miroslav Klose and Gotze missed the chance to double Germany's lead, but Chile ended the half strongly with Toni Kroos and Marcel Schmelzer having to make timely interventions to deny Charles Aranguiz and Vidal respectively.
The visitors continued to press forward after the interval and Vargas' strike came back off the woodwork to frustrate Jorge Sampaoli's side.
Alexis Sanchez's strike from point-blank range produced a fantastic save from Neuer, who also improvised to save with his feet from the Barcelona forward's long range strike shortly afterwards.
Felipe Gutierrez's speculative volley from the edge of the area missed the target as Chile came on strong in the closing stages, yet they failed to make their dominance count in the final third as the match approached its closing stages.
The closest they came was when Fabian Orellana thumped over from just outside the area as Germany's backline defended stoutly to preserve victory.