Diaz's momentary lapse in concentration last night let Timo Werner rob him of possession, draw the goalkeeper and pass to Stindl, who scored into an empty net on 20 minutes in Saint Petersburg.
"Unbelievable," beamed Germany captain Julian Draxler, who won the Golden Ball for the tournament's best player.
"We fought well and deserved this win. We hadn't played together before the tournament, which makes it even more valuable.
"Every title is special, but with this young team, it's even more so.
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This is the first time Germany, the defending world champions, have won the Confederations Cup in the eighth edition of the pre-World Cup tournament.
"There was not much difference between the two teams," said Chile captain Claudio Bravo, voted the tournament's best goalkeeper.
"We are sad not to have won, but we played against a world-class team and must learn from our mistakes."
The video assistant referee (VAR) again came into the spotlight as Chile's Gonzalo Jara was lucky not to be sent off in the second half.
Werner, Stindl and Leon Goretzka all finished with three goals but RB Leipzig striker Werner took the top scorer's prize by virtue of also supplying two assists.
Despite dominating for long spells, Chile failed to turn 61 per cent possession and 20 shots -- compared to the Germans' eight -- into goals.
The South Americans kept the same team which squeezed past Portugal 3-0 on a penalty shoot out after a goalless draw in the semi-finals.
Meanwhile, Germany's only change from the team which beat Mexico 4-1 in the last four saw defender Shkodran Mustafi replace Benjamin Henrichs.
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Chilean fans turned the Saint Petersburg Stadium into a sea of red and merciless pressing by La Roja early on saw Charles Aranguiz and Arturo Vidal cause havoc in the Germany defence.
Eduardo Vargas had the first clear shot on 11 minutes which flew into the grateful arms of Germany goalkeeper Marc- Andre ter Stegen.
The South Americans then wasted a golden chance when Vidal's shot was blocked by Ter Stegen and Alexis Sanchez could not connect with the loose ball.
It proved costly as Diaz's calamitous mistake and Werner's quick thinking led to Stindl's match-winner.
Having fallen behind, Chile upped the pressure to force an equaliser which left space at the back for Germany to counter-attack.
Draxler fired wide of the post, then Goretzka, who scored twice in the 4-1 semi-final win over Mexico, wasted a great chance by firing straight at Bravo just before the break.
Chilean tempers started to fray, and approaching the hour mark Joshua Kimmich squared up to Vidal, who pushed the German away. The Bayern Munich team-mates were both booked.
The South Americans battered the German goal in the final 20 minutes but Sanchez's shot was blocked and Ter Stegen then saved from Vargas.
With time running out, both Vidal and substitute Angelo Sagal fired over the bar, as the German defence held firm.