The 18-year-old beat Inter's offside trap and slotted home the winner from an acute angle just a minute before half-time, following fine work from midfielder Marco Verratti.
The result was just reward for PSG's dominant performance although they were made to work for their win by the Italian league leaders.
Despite being a friendly, both sides could have scored on several occasions and there was enough entertainment for the Doha crowd.
Italian Cup: Inter cruise into last-eight
Augustin, who had played only six times for PSG before Wednesday, himself should have scored after just 36 seconds, missing a great chance by blazing over from some 15 yards when clean through on Inter's goal.
Star draw Zlatan Ibrahimovic, booed by some Inter fans, also went close forcing a fine save from Samir Handanovic in the 13th minute.
But despite their dominance of possession, PSG were opened up several times by Inter and the Italians almost broke the deadlock in the 18th minute when Martin Montoya was denied by Kevin Trapp.
Closest of all before the goal though was Verratti who thundered a shot against the bar in the 29th minute, with Handanovic well beaten.
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The match largely fizzled out in the second half -- though there were chances for PSG's Adrien Rabiot and Inter's Stevan Jovetic -- as both teams made wholesale changes.
Inter almost forced an equaliser through Yuto Nagatomo in the 81st minute, but Trapp denied the Italians again.
Inter, who started with just five players from the team which lost 2-1 at home to Lazio in their last league outing on December 20, made 10 substitutions in the second period.
PSG made five, with Ibrahimovic going off in the 64th minute to a mixture of cheers and jeers.
Notably, PSG coach Laurent Blanc did not bring on almost all of his South American stars who had jetted into Qatar just over 24 hours before.
Despite reports that the match was a 15,000 sell-out and it being the most high-profile match played in Qatar throughout the year, only 11,628 fans turned up to watch, with the ground largely emptying before the end.
The game brought the curtain down on PSG's four-day winter tour to Qatar.
The runaway Ligue 1 leaders return to action on January 9 against Bastia.
Inter play again on January 6 against Empoli in Serie A.
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