German Cano's header from close range gave Fluminense an early lead, and they then withstood an onslaught from the Italian side in the second half before substitute Hercules sealed their victory late on.
The Rio de Janeiro outfit, who qualified for the Club World Cup thanks to their Copa Libertadores triumph in 2023, became the second Brazilian side to make the last eight after Palmeiras.
Captained by 40-year-old former PSG and Chelsea centre-back Thiago Silva, 'Flu' will now go to Orlando for a tie against Al-Hilal.
Stefan de Vrij prodded wide from close range and captain Lautaro Martinez saw a fine shot on the turn from the edge of the box come back off an upright, and confirmation that it would not be Inter's day arrived in stoppage time. As a substitute, Hercules pounced on a falling ball and drove into the box before firing low into the corner.