Weary Sinner happy for day off after battling into Shanghai last 16
He will be joined in the last 16 by Daniil Medvedev, who also had to rally to overcome tenacious Italian Matteo Arnaldi 5-7, 6-4, 6-4.
A weary-looking Sinner dropped the first set on a tiebreak to the 37th-ranked Etcheverry, just three days after losing a 3hr 21min China Open final in Beijing to Carlos Alcaraz.
But the 23-year-old recovered in the second set, breaking Etcheverry twice to level the match before easing to victory.
"Tomorrow is one day off which I really need, I felt it physically today," Sinner said.
"I had some chances in first set but couldn't use them... I'm very happy with how I bounced back," he added.
World number five Medvedev broke early in the first set but 36th-ranked Arnaldi kept his cool to break back in the sixth game on an unforced error from the Russian.
Arnaldi broke again in the 12th game after Medvedev hit long.
The Russian's mood darkened under pressure from Arnaldi in the second set and he was slapped with two code violations and a point penalty after arguing with the umpire.
The 28-year-old former world number one recovered to take the match to a deciding set and came through after 2hr 44min.
"I was expecting him to play differently, he played very good," Medvedev said of Arnaldi.
"To be honest in the first set I should have done better. The second and third were even closer... but at the end I'm happy to win."
Play was only possible under the roof of the main court as rain forced matches on the outside courts to be postponed for the second day in a row.