The win provides the Australian and world No.9 with valuable points as he chases qualification for the elite eight-man ATP Finals in mid-November for a third successive year.
Earlier losses in Shanghai by other main drawcards such as Francis Tiafoe, Arthur Fils and Novak Djokovic further boost those chances.
On reaching the quarters, de Minaur was on target for a berth in the mid-November ATP finals in Turin, sitting seventh in the live rankings.
De Minaur, who reached the semi-finals at the season-ending tournament in 2025, also reached the China Open final last week in Beijing against Novak Djokovic, where he retired injured when a set down.
The Australian broke Khachanov in the eighth game of the first set in Shanghai on Tuesday, producing his trademark court coverage and nous before hammering a double-handed backhand down the line, bringing mentor and Davis Cup captain Lleyton Hewitt to his feet in the stands.
De Minaur then romped through the next game as he served for the first set, taking it with an ace when up 40-0.
He broke the 26th-seeded Russian Khachanov to go up 2-1 in the second set and then again held to love.
De Minaur's brilliant groundstrokes and coverage continued as he went up 5-3, often drawing gasps and hearty applause from the crowd in Shanghai.
Khachanov dug in when he could and forced de Minaur to work hard to serve out the match, which he did after saving a break point, taking the second 6-4.
The 27-year-old let out a roar after the straight-sets win as he marched into the last eight, where he will play either world No.2 Alexander Zverev or Kazakhstan's Alexander Bublik.
France's 56th-ranked Arthur Gea also reached the quarters, with an upset 7-6 (7-4 6-4 win over 13th seed Jakub Mensik of Czechia.
11°C