
The 22-year-old Canadian is attempting to capture a fourth title in as many weeks after victories in Florence, Antwerp and Basel last month.
Having raced through the opening set against the 21st-ranked Tiafoe, Auger-Aliassime needed six match points to finally see off the American.
Auger-Aliassime is through to his second Masters 1000 semifinal and will play either world No 1 Carlos Alcaraz or Danish teenager Holger Rune for a place in Sunday’s championship match.
The eighth-seeded Auger-Aliassime has enjoyed a breakout season.
His 56 wins are third most on the ATP Tour this year, while only Alcaraz has bettered his four singles titles.
Defending champion Novak Djokovic takes on Italy’s Lorenzo Musetti in the quarterfinals.
Tommy Paul, who dumped out Rafael Nadal in the second round, will look to cause another surprise when he goes up against fifth seed Stefanos Tsitsipas.