Joachim Low's charges held onto a narrow lead to beat Jorge Sampaoli's men in the Mercedez-Bens Arena on Wednesday night
Joachim Low's side are one of the favourites for the showpiece in Brazil later this year, having eased to nine wins and a draw in an unbeaten qualifying campaign.
Yet, in an era when they have been rightly lauded for their new-found attacking style, Germany were forced to rely on the methods of their predecessors when sneaking the spoils against a Chile side who lent further weight to the theory that they will be a match for anybody when the tournament starts in June.
On a night when much of the focus centred on whether Miroslav Klose could grab the one goal required to become Germany's most prolific marksman of all time, it was Gotze who earned the victory.
The fact that Klose, who was withdrawn at half-time, remains level with the legendary Gerd Muller on 68 goals will not detract from an impressive win for Low's men.
Indeed, a contest between two free-flowing teams lived up to its billing as both sides showed glimpses of their prowess.
It was the South American side, who impressed in coming through the tough qualifying group to reach the World Cup, that started the brighter.
Germany seemed particularly confused by the visitors' 3-3-1-3 formation as Chile's fluidity repeatedly caught their opponents out.
One of their counter-attacks almost led to an opener as Gonzalo Jara's excellent diagonal ball found Mauricio Isla, whose cross was intercepted by Jerome Boateng with Barcelona's Alexis Sanchez lurking for a simple tap-in.
Philipp Lahm had to be on high alert too a few moments later when clearing off the line after Arturo Vidal had met the resulting corner with a bullet header.
Soon afterwards, though, Germany took the lead against the run of play.
Mesut Ozil played a fine one-two with Bastian Schweinsteiger on the edge of the box before sliding across to Gotze, who controlled quickly with his right foot and lifted the ball into the top corner with his left.
Chile should have levelled in the 26th minute but Vidal struck straight at the goalkeeper from close range after a rare Schweinsteiger error.
The famous goal that man-of-the-moment Klose craved almost came, albeit in fortuitous fashion, as the striker mis-controlled Kevin Grosskreutz's powerful effort towards goal to force a solid, diving stop from Johnny Herrera.
Germany came even closer to doubling their tally when Gotze found space in the area, yet he curled narrowly wide.
Much like the opening period, Chile came out of the blocks quickly after half-time and created a series of half-chances.
Their best opening fell to Sanchez, only for the Barcelona forward to hit the woodwork as the visitors continued to be frustrated.
Manuel Neuer's goal was under siege for the remainder of the half but a resolute defence was on hand to produce a series of last-ditch blocks as Germany sealed the win.