They led by one stroke from American Stewart Cink, while Australian former world number one Adam Scott surged to within four strokes with a late rush to match the day’s best round, a 64.
But world number nine Rickie Fowler, the top-ranked player in the field, can get an early start to Erin Hills for next week’s U.S. Open in Wisconsin after missing the cut with rounds of 74 and 70.
Schwartzel, who finished a quiet third at the Masters in April at Augusta National, continued a run of good form which he credited to improvements on the greens.
"Last year I wasn’t putting well,” he told Golf Channel. “I identified the problem and switched putters, thought about all the things I did as a junior. I used to putt really well as a junior.
"It feels like I’ve got my own natural stroke back, stays lower to the ground and scoring is showing."
Munoz, who shared the lead after the first round, stayed at the top of the leaderboard after a tidy 67 that included a lone bogey.
"I’ve been pretty consistent with my tee shots, putting the ball in the fairway and getting the ball on the green, capitalising on some putts and if not just tap in for par," said the PGA Tour rookie.
He has found it difficult to get into a competitive rhythm this season because his low ranking reduces his playing opportunities, but says he is finally starting to find his comfort zone.
Scott, meanwhile, was closer to the cut line than the lead for much of the day, but he stormed home with an eagle and two birdies in the final five holes to jump to equal 11th.
A seven-iron that did everything but go in at the par-three 14th set the tone for his hot finish.
“I’ll take a tap-in (birdie) any day on that hole,” said the 2013 Masters champion. “If I made a few more putts it would have been a real special round.”
(Reporting by Andrew Both in Cary, North Carolina)
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