The Spaniard began the day in a tie for the lead on nine under par but found himself well behind home favourite Jayden Schaper by the time he teed off at 11.30.
A lightning-fast start saw him close the gap, though, as he went agonisingly close to opening his second round with an albatross but instead had to settle for an eagle.
He led by one shot at the turn after adding three front-nine birdies but back-to-back bogeys on the ninth and tenth saw him slip from the summit.
But Chacarra responded by making three more birdies on the way in to reach 15 under par and lead by two at the halfway stage.
In-form Schaper was his nearest challenger on 13 under after firing a bogey-free 64, one ahead of countryman Branden Grace and England's John Parry.
After Chacarra's opening tee-shot landed among the trees on Friday, it had looked like he would not be able to go for the green in two.
But he proved the doubters wrong by going straight at the flag and hitting the hole with his second shot, missing out on an albatross by the smallest of margins before holing the return putt for an eagle.
The 2025 Hero Indian Open champion kept the fireworks coming at the third as he holed his enormous birdie putt to get within one shot of the lead.
After birdieing the sixth from five feet to join Schaper at the top, he hit the front on his own with a tap-in on the eighth.
Chacarra dropped his first shot of the day on the tenth before surrendering another bogey at the 11th but got one of the strokes back at the short 12th.
He also took advantage of the par-three 16th with a fine birdie putt from the fringe to lead on his own once more, while a closing birdie handed him a two-shot cushion.
Chacarra said: "There's a lot of golf left.
"It's a course where people can go low and if you don't have your best you can go high.
"So everyone can win, there's a lot of guys out there.
"I'm just going to try to do my best, get a game plan with my caddie and I know if I execute and I play like I did these two days, I'm going to have a good chance coming out on Sunday."
South African Christiaan Burke and Spain's Eugenio Chacarra both posted record scores at Royal Johannesburg Club to share the first-round lead at the 2026 Alfred Dunhill Championship.
South Africa's Shaun Norris is relishing his chance to defend the Alfred Dunhill Championship title at Royal Johannesburg this weekend.
Rasmus Neergaard-Petersen held off a challenge from local hopeful Cam Smith to claim his maiden DP World Tour title at the 2026 Crown Australian Open on Sunday.
Kristoffer Reitan held off the chasing Jayden Schaper and Dan Bradbury to claim the Nedbank Golf Challenge at the picturesque Gary Player Country Club on Sunday afternoon.
