Wimbledon champion Murray, who clutched at his right shoulder after going an early break down to trail 3-2 in the first set, soon snapped into focus to run off four games in a row on his way to a 6-3 6-2 victory.
Showing off his dazzling variety of shots and remarkable court coverage, Murray extended his winning streak to 20 with his 600th career victory on the ATP Tour.
The Scot said breaking back straight away was vital.
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"It was big, obviously," Murray said. "When you're playing against big servers they tend to be front runners, so for me to get the break back immediately was key and it got the momentum back."
Third-seeded Nadal, showing fatigue following a busy Olympic schedule that included a gold medal in doubles, was a step off the pace and paid the price against 19-year-old Borna Coric of Croatia, who reached the last eight with a 6-1 6-3 win.
Elsewhere, Grigor Dimitrov eliminated sluggish second seed Wawrinka, the Bulgarian making the most of a single break of serve in each set to win 6-4 6-4 and book his berth in the quarters.
Australian Bernard Tomic, 23, notched yet another upset with a 7-6(1) 7-6(5) win over fifth-seeded Kei Nishikori of Japan, who had won the bronze medal match in Rio over Nadal.
Tomic's next assignment will be against Murray, who owns a 4-0 advantage over the Australian in head-to-head encounters.
'PLEASE MISS'
Coric advanced to his first ATP World Tour Masters 1000 quarter-final, dominating 14-times grand slam winner Nadal by reeling off 10 straight games to claim the opening set and lead 4-0 in the second.
Nadal received treatment on his left wrist after the first set and continued to fight.
"It was an unbelievable match on my side. I think he wasn't playing his best tennis," said Coric, who won the junior U.S. Open title in 2013.
The Spaniard rallied towards the end before a relieved Coric closed it out on his second match point with a backhand winner.
"I was thinking, 'Rafa please miss, I cannot make a winner'," he said of Nadal's fightback.
Next up for Coric is compatriot Marin Cilic, who ousted sixth-seeded Czech Tomas Berdych in three sets.
Dimitrov, 25, who has struggled for consistency, was buoyed by his performance against doubles partner Wawrinka.
"I need matches like that," Dimitrov said. "I need 10 or 12 more of those matches to sustain that level and also to send a statement not only for me, but towards everyone."
The Bulgarian will next face American Steve Johnson, who saved four set points as he advanced to the quarters over seventh seed Jo-Wilfried Tsonga of France 6-3 7-6(6).
(Reporting by Larry Fine in New York; Editing by Andrew Both/John O'Brien)
