Germany struck against the run of play when Mesut Ozil did well to tee up Goetze, whose controlled finished beat Johnny Herrera from 12 yards.
Inspired by the tricky Alexis Sanchez and powerful Arturo Vidal, Chile created chance after chance but could not finish the host of openings that passed them by.
Vidal, who ended the game limping and holding his hamstring, squandered Chile's best opportunities of the first half, the best of which was a free header from Sanchez's corner that was cleared off the line.
Germany couldn't get to grips with Chile's slick counter-attacks and relied on Jerome Boateng and Per Mertersacker's countless clearances.
Chile could have drawn level when Eduardo Vargas beat Manuel Neuer with a crisp shot on the turn - only to see it strike the underside of the bar.
Germany somehow came through the match unscathed but it was a far from convincing display by Die Nationalmannschaft, while Chile delivered a reminder that they can be a force in Brazil.
9' CHILE CHANCE - Brilliant counter-attack by the visitors again but Vidal delays his cross to Sanchez and Boateng clears before it reaches the Barca man, who is slapping his thighs in frustration that the cross wasn't made earlier.
15' GOAL! - Goetze gives Germany the lead against the run of play! Ozil untangles the ball from under his feet to find Goetze, who guides the ball into the top corner from 12 yards.
26' CHILE CHANCE - Should be 1-1! Vidal squanders Chile's best chance of the game as he can only send a tame effort straight at Neuer after he was teed up from the right.
43' CHILE CHANCE - Chance for Chile as Aranguiz turns his marker, but drills just wide from close range.
44' CHILE CHANCE - Yet another chance for the Chileans and it's another for the unmarked Vidal, who leaps highest to meet a corner, but heads wide.
61' OFF THE BAR! Vargas hits the underside of the bar with a super snap shot on the swivel from 10 yards. Superb play by Sanchez to create the chance.
69' GERMANY CHANCE - Ozil's smart flick finds Goetze but the Bayern forward is smothered by the on rushing Herrera.
Germany have now won five of their last six games.
This is the first time Chile have failed to score in their last 13 games.
TALKING POINT: Can Chile make an impact in Brazil? On this evidence, most certainly yes - but they need a striker that they can rely on. Sanchez created chance after chance but the South Americans failed to get the goal their performance deserved. But there is clear evidence that Australia, Spain and the Netherlands will not get any easy ride against Vidal and co.
MAN OF THE MATCH
Jerome Boateng (Germany): Made countless clearances as Chile put Germany under huge pressure throughout. While Germany struggled in midfield and attack, Boateng's display alongside Mertersacker was impressive.
Germany: Neuer 6, Grosskreutz 7, Mertesacker 8, Boateng 9, Jansen 6, Lahm 6, Schweinsteiger 6, Goetze 7, Kroos 6, Oezil 7, Klose 5. Subs: Schmelzer 7, Ginter N/A, Schuerrle 6, Podolski N/A
Chile: Herrera 7, Isla 7, Medel 7, Jara 7, Beausejour 7, Aránguiz 6, Silva 7, Gutiérrez 7, Vidal 8, Vargas 8, Alexis Sanchez 8. Subs: M Gonzalez 6, Pinilla N/A, Valdilvia 7, Fernandez N/A, Orellana 6
THE MATCH IN A TWEET
- Sports & Recreation
- Mario Goetze
- Alexis Sanchez
- Jerome Boateng
- Arturo Vidal
- Mesut Ozil