the Canadian struck a crosscourt inside out forehand winner to break serve to reach 4-2.
Auger-Aliassime had previously been 0 of 8 in breakpoint conversions for the night.
With Tiafoe serving to stay in set two at 2-5, the Canadian struck an overhead winner before the American netted a crosscourt forehand half volley to drop the set.
Tiafoe rebounded in set three; striking powerful down the line forehand winners and serves at speeds of 139 miles per hour to save three set points and reach the tiebreaker.
The tiebreaker featured the majority of serves in the 120-130 miles per hour range which set up powerful volleys and groundstroke winners.
Serving down set point at 5-6, the Canadian struck a 121 miles per hour down the tee serve which Tiafoe netted with a down the middle forehand return.
Auger-Aliassime then struck a 117 miles per hour serve out wide which Tiafoe returned long with a forehand crosscourt to face set point at 6-7.
The American missed his first serve and then struck a 76 miles per hour second serve before netting a crosscourt forehand to drop the set 7-6 (8-6).
The Canadian broke serve to open the final set.
The two players then held their following service games to reach 5-4.
Serving for the match, the Canadian struck two serves at 126 and 124 miles per hour before double faulting to reach 30-15.
Auger-Aliassime struck a 125 miles per hour ace down the tee, his 24th and final ace of the night to reach matchpoint at 40-30.
The Canadian then struck a 116 miles per hour serve down the tee which he followed up with a crosscourt forehand winner to end the match after three hours and twenty-three minutes of play.
The two tour friends then shook hands and hugged at the net.
The 23 year old Tiafoe began the match as the stronger player.
However he finished with 36 unforced errors and converted only one of five breakpoint chances.
With his coach Tony Nadal watching, the 21 year old Auger-Aliassime struck 55 winners and saved four of the five breakpoints he faced to reach his second career grand slam quarterfinal after reaching the Wimbledon quarterfinals in July.
Tiafoe posted his greatest career grand slam result in reaching the quarterfinals at the 2019 Australian Open.