The 41-year-old was one-under when he made the turn but then scorched the course by picking up six birdies on his final eight holes to end with a two-day total of 131.
Fellow American Xander Schauffele, who started a shot behind overnight leader Cameron Smith of Australia, carded a 67 to sit a shot behind Perez.
"I didn't think I really played that well. I got off to a slow start, we had the break obviously and just went out, and I like the front, I play better on the front," Perez said.
"Just made some decent shots and I putted pretty well today. My short game was good so that saved me."
The event, co-sanctioned by the PGA and Asian Tours, features a smaller than usual field and there is no cut with the 78 players scheduled to complete all four rounds.
Players were taken off the course during the second round due to the threat of lightning, which caused a delay of close to four hours.
Overnight leader Smith struggled during his second round of 71 and slipped down to a share of third spot with South Korean Sung Kang (68) and Belgian Thomas Pieters (67).
World number three Hideki Matsuyama, who was in the same group as Perez, carded a 68 and was tied for eighth after starting his round with two birdies in three holes.
American Justin Thomas, who has won the tournament for the last two years with a combined score of 49-under, was tied for 33rd after following up his opening round of 70 with a 71.
"I'm going to try to hit it better," Perez said.
"You're going to have to putt well anyway. Anytime you're trying to win you've got to putt well. So the guy that wins hits it pretty good, but he putts the best, he scores the best.
"I've got to try to do the same thing on the weekend. Obviously Justin, as he did it with low scores last year, the last two years."
(Reporting by Sudipto Ganguly in Mumbai; editing by Toby Davis)
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