The 37-year-old Mannarino, who has won more matches on grass than any other Frenchman, pushed De Minaur hard but ran out of steam against the pace and consistency of the world number six.
"Super tough... I'm super happy. I found a way after a very tricky start," said De Minaur.
"I knew that I wasn't safe until the last point. I kept that intensity and focus and it made it worth it in the end," he added.
It was the Frenchman who started the stronger, breaking De Minaur's first service game and racing into a 3-0 lead, capitalising on some uncharacteristic errors from the Australian.
Falling behind seemed to galvanise the younger man, who won his next service game to love and broke back immediately after a costly double fault by Mannarino.
Mannarino delighted the crowd with an extraordinary behind-the-back shot that helped him win another break of serve, but again he failed to consolidate his advantage, pushing a backhand long to give up a break of his own.
The turning point of the first set came at 4-4 when De Minaur showed off his trademark speed to recover a delightful crosscourt drop shot, winning another break of serve and giving himself the chance to serve for the set.
The Australian converted at the first time of asking, helped by two timely aces, to take a competitive first set 6-4.
Losing the set seemed to knock the stuffing out of Mannarino, who was broken in his two opening service games, showing his frustration by smashing a ball into the crowd.
A third service break followed and De Minaur completed the "bagel" 6-0 set, wrapping up the match in one hour 20 minutes.
De Minaur, hoping to repeat his 2024 championship win here, is the top seed left in the draw after the shock defeat on Friday of world number four, Felix Auger-Aliassime.
The Canadian lost 6-4, 6-3 to Poland's Kamil Majchrzak, who plays Russia's Daniil Medvedev in Saturday's other semi-final.
Check out the full match statistics on Flashscore
