The Scot had to break serve just to stay in the first set at 6-5 down, before going on to take it on a tie-break.
He booked his place in the last eight with a 6-4 victory in the second, which sets up a meeting with Juan Martin del Potro.
The world number three said that it was a close match against an opponent who played very aggressive tennis.
"It was tough," ESPN quotes Murray as saying. "He started well and he was playing very aggressive. He had a lot of chances in the first set. He obviously served for it.
"The second set was kind of the other way around. I had a lot of chances, but it was still tight. All the games were pretty close, a lot of long games and longish rallies."