"He's a tricky opponent... a super-experienced player," said Dimitrov.
"I definitely had to stay away a little bit from that forehand. I knew if I kept the ball low on his backhand side and just kind of worked my way into the court, it would be the right thing to do. I think I did this thing very, very well today."
Dimitrov will bid for a place in the semi-finals for the second straight year when he faces Japan's Yuichi Sugita, who reached his first Masters 1000 quarter-final.
The unseeded Sugita overcame Russian Karen Khachanov 6-7(0) 6-3 6-3 before a thunderstorm forced play to be suspended for more than two hours.
The 28-year-old Japanese captured his first ATP World Tour title at the Antalya Open in July, adding to three ATP Challenger Tour events won in 2017.
"He's been playing really well," said Dimitrov. "He's going to be definitely a tough opponent to play."
Dimitrov got off to a great start by opening up a 3-0 lead against Del Potro.
Del Potro mirrored Dimitrov by winning the first three games of the second set but could not convert three set point chances at 5-4, before the Argentine began to struggle in the heat.
A doctor was called at the 6-5 changeover, but Del Potro was determined to finish the match.
Dimitrov improved to 31-14 for the season, which includes two ATP World Tour titles.
In later games, John Isner never dropped a service game on his way to a 7-6(4) 7-5 win over fellow American Frances Tiafoe.
Isner rocketed two aces to close out the match and punch his card to the quarter-finals, where he will face another American in Jared Donaldson.
Donaldson, who defeated Nikoloz Basilashvili in straight sets on Thursday, will be one of four unseeded players in the quarters following a series of upsets early in the tournament.
Third seed Dominic Thiem needed two tie breakers to dispatch France's Adrian Mannarino 7-6(4) 7-6(3) and set up a meeting with Spain's David Ferrer, who upset 11th-seeded Pablo Carreno Busta 6-4 6-4.
Rain put a halt of Australian Nick Kyrgios' match against Ivo Karlovic with the Croatian leading 4-3 in the first set.
Wet weather also postponed the start of top-seeded Rafael Nadal's match against fellow Spaniard Albert Ramos Vinolas.
(Reporting by Larry Fine in Tampa and Rory Carroll in Los Angeles; Editing by Ken Ferris/Peter Rutherford)
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