"I felt good in the first match", the 36-year-old said.
The Spanish world number one defeated Dimitrov en route to winning the China Open last week and he repeated the success with a 6-4 6-7 (6/8) 6-3 win on Friday, extending his winning streak to 15 matches.
Rafael Nadal has tied Andre Agassi for sixth place on the list of Open Era wins by reaching the Shanghai Masters semi-finals.
The Argentine recovered from a slow start to triumph 4-6, 6-1, 6-4.
The final set was full of momentum shifts, first starting with Dimitrov's break of serve in the opening game as he carried over the momentum from the second set.
Del Potro, pushed to the brink of retirement by four wrist surgeries that saw his ranking slip as low as 1,045 at one point in his career, said Zverev would learn.
And he underlined his status as the man to beat in Shanghai as he battered the Italian Fognini 6-3, 6-1.
Dimitrov extended the quarter-final to a third set when he rebounded from a 4-2 deficit to win the second-set tiebreaker.
Fourth-seeded Marin Cilic stands between Nadal and a second ATP final in two weeks. "I think it was a great battle between two players who are playing all the time very focused".
The 2014 US Open champion knocked out Spain's unseeded hopeful Albert Ramos, 6-3, 6-4.