Palmer and Garcia shared the second-round lead at 8-under 132 after a sun-soaked round Friday when the wind was gusting up to 36 mph.
Garcia posted his second consecutive 4-under 66, after withdrawing from a British Open qualifier five holes in and passing up a practice round at TPC Four Seasons because of an infected fingernail on his left hand.
After a bogey at the 523-yard par-4 third hole when his approach flew over the green, Garcia birdied three of the next four holes and was bogey-free the rest of his round. Despite the windy conditions, he hit 11 of 14 fairways and 14 of 18 greens.
"You would be happy with those stats on a day with not much wind," Garcia said.
There also were some impressive shots along the way for Garcia. The 31-year-old Spaniard blasted out of a greenside bunker to 7 feet to save par at No. 14, then had a 45-foot chip-in birdie at the 15th hole when he couldn't putt because of three sprinkler heads in the way. Walking into the stiff wind the rest of the way, he had pars on the last three holes.
Palmer shot a 67. He had made the cut only once his seven previous appearances at the Nelson with nine consecutive rounds over par before this week when caddie James Edmondson is calling his shots.
"He's never played good here and we finally decided that I was going to take over and just lead the horse around the ranch," Edmondson said.
With input from instructor Randy Smith, Edmondson is telling Palmer where to hit off the tee and what to do with his approach shots. The arrangement is working so far. Palmer opened with a 65 Thursday before what was maybe a more impressive round with only one bogey in difficult conditions.
"I keep surprising myself how calm I am when it's that way. ... This is a golf course that I've struggled on so it's nice to not to think about it, just get up and hit the shot, and if I don't hit the shots it's on me," Palmer said. "So it's nice to be free-swinging like that."
For the second year in a row, area amateur teenager Jordan Spieth made the cut at the Nelson. After his 2-under 68 Friday, he was in a group of six players at 3 under.
Spieth's high school graduation ceremony is Saturday afternoon. The ceremony for Dallas' Jesuit Prep's graduating class of 246 seniors starts at 4 p.m. Saturday, at an auditorium on the SMU campus about 20 miles from TPC Four Seasons.
"Right after the round ... I'm going to shoot over there as quickly as possible," Spieth said. "I don't know how long (graduation) usually lasts."
First-round leader Jeff Overton followed his opening 64 with a 74 that including consecutive bogeys to end his round.
Seventy-four players made the cut at 3 over. Right on that mark was defending champion Jason Day (71).
Palmer had his only bogey at the 503-yard, par-4 15th hole when he missed the green with his approach and then two-putted from 17 feet. With the wind really starting to pick up he parred out, using a 5-wood for the second consecutive day at No. 18, where he had a 25-foot birdie attempt just slide by the cup.
"I thought I was going to hit driver today and (Edmondson) pulls that 5-wood. `What am I going to do, hit 5-wood? Five-wood?" Palmer said. "And he goes. `Let's practice for the British Open. Hit the 5-wood hard, you can hit,' and I did that. Hit a perfect 5-iron to the middle of the green."
Garcia, the 2004 Nelson champion, hasn't won a tournament since 2008.
"When I'm feeling good, even in windy conditions like today, I feel like I can control the ball flight and I can hit some good, solid shots," Garcia said. "It's going to be tough out there. I just need to make sure that I stay positive and just try to trust myself as much as I can."