The fifth seed produced a commanding performance to beat the Greek 6-4, 7-5 in one hour and 24 minutes, maintaining his composure throughout a contest in which he did not face a single break point.
The victory extended Medvedev's head-to-head advantage over Tsitsipas to 11 wins in their 16 meetings on the ATP Tour and kept the Russian's hopes of winning a second Shanghai title alive.
Medvedev dominates on serve
Medvedev established control early in the match, applying pressure on Tsitsipas and making the most of his opportunities from the baseline.
The Russian took the opening set 6-4 after consistently challenging his opponent's serve and limiting the Greek's opportunities to dictate rallies.
Medvedev's serving was particularly effective, as he held all his service games without facing a break point. His ability to win points behind his first serve and attack Tsitsipas's backhand helped him maintain the advantage.
Reflecting on his performance, Medvedev said he felt he had played very well and put significant pressure on Tsitsipas during the opening set.
Russian seals victory in tight second set
Tsitsipas raised his level in the second set, making the contest more competitive as both players looked to gain the decisive advantage.
However, Medvedev remained composed in the crucial moments. He secured the decisive break to move ahead 6-5 before serving out the match to complete a 6-4, 7-5 victory.
The 30-year-old said the second set had been much tighter but expressed satisfaction with his returning and the rhythm he found during the closing stages.
The result demonstrated Medvedev's ability to manage pressure against an experienced opponent and move into the last eight without dropping a set in the tournament.
Medvedev continues impressive Shanghai record
The victory marked another significant milestone for Medvedev in Shanghai, where he won the title in 2019.
He reached the quarter-finals for the fourth time in his past five appearances at the tournament and continued his pursuit of another ATP Masters 1000 crown.
Medvedev was also the only former Shanghai champion remaining in the draw at this stage, increasing his opportunity to challenge for the title as the competition progressed.
His run in China could also prove important in the race to qualify for the ATP Finals in Turin, with the Russian seeking another appearance at the season-ending championship.
Tommy Paul awaits in the quarter-finals
Medvedev's next opponent will be American Tommy Paul, who defeated Belgium's Zizou Bergs 7-6(5), 6-4 to secure his quarter-final place.
Paul had to withstand a second-set fightback from Bergs, who had eliminated second seed Carlos Alcaraz in the previous round. The American nevertheless held on to complete the victory and arrange a meeting with Medvedev.
The quarter-final presents Medvedev with another test as he seeks to convert his strong form into a deep run at the Shanghai Masters.
Other Shanghai Masters results
Elsewhere, Spanish youngster Rafael Jodar continued his impressive campaign by coming from a set down to defeat Botic van de Zandschulp 6-7(4), 6-4, 6-2.
Jodar will face Norway's Casper Ruud in the quarter-finals after the former French Open finalist advanced when fourth seed Felix Auger-Aliassime retired with an apparent knee problem while trailing 5-2 in the opening set.
Paul's victory over Bergs also completed the quarter-final match-up against Medvedev, while the top half of the draw featured Alexander Zverev against Alex de Minaur and Arthur Gea against Alejandro Davidovich Fokina.
With several leading contenders already eliminated, Medvedev will look to take advantage of the opportunity and add another major hard-court title to his collection.