Neither, however, own the tournament lead as Daniel Brooks was 4-under on the day and has a one-stroke lead going into Saturday's play.
Campillo, 27, and yet to win a professional tournament, had two eagles, seven birdies and nine pars. He was 4-under on the par 3s at the Mount Edgecombe Country Club in Durban and had eagles at the 558-yard, par-5 12th and the 292-yard, par-4 fourth.
Nel, 30, and also looking for his first European Tour win, had an eagle -- also on 12 -- nine birdies and eight pars for his 59.
No golfer has turned in a 59 on the European Tour and the feats Friday by Campillo and Nel won't be listed as the record because soggy course conditions allowed players to place the ball.
The tournament has been plagued by wet conditions and water-logged fairways that led officials to delay Friday's start of play for 3 hours. There was another 3-hour suspension at midday and play was called because of darkness with about half the field still to complete the second round. The event has been reduced to 54 holes due to the backlog.
Brooks, who led after the first round finally wrapped up, played 11 holes Friday and was 4-under for the second round, which took him to 12-under for the tournament.
Campillo's 11-under score followed a first round of even-par 70 and had him tied for second. Matthew Baldwin, with a second-round 62, is also 11-under 129 after 36 holes.
Oliver Bekker and Branden Grace each shot 4-under 66 in the second round and are tied for third at 10-under 130 for the tournament. Also at 10-under overall is Dawie van der Walt, who was 7-under through 13 holes of the second round.
Nel had a first-round of 7-under 77 so his 59 only pulled him to 4-under and a tie for 27th in the overall standings.
Campillo, starting on the 10th hole for the second round, birdied the par-3 11th before the eagle at 12. He added birdies at 14 and 15 and made the turn in 31.
His front-side 28 began with a first-hole birdie and his card read 2-2-2 over Nos. 3-5, a pair of par 3s and the par-4 fourth. A birdie at the eighth hole gave him the 59.
Nel had five front-side birdies and three consecutive birdies after the eagle at 12 for an 11-under through 15, but he had pars the final three holes.
The all-time low professional score is 12-under 58 by Ryo Ishikawa in 2010 on the Japan Golf Tour and 59 has been recorded 14 times on other major tours but Friday marked the first time in the European Tour.
The first to shoot 59 was Al Geiberger on a PGA Tour event in 1977 and, most recently, Jim Furyk shot 12-under 59 at the 2013 BMW Championship.