Baldwin had been four shots off the pace at the halfway stage but made back-to-back birdies at the fifth and sixth before picking up further shots on the 10th and 13th to grab a share of the lead on 11 under par before play was suspended due to darkness on Saturday evening.
The 37-year-old, who is searching for his maiden DP World Tour title in South Africa this week, narrowly missed his birdie try on the 14th before fading light brought a halt to proceedings.
He will return to the course to complete the back nine at 8am on Sunday before beginning the fourth round.
Norwegian Johannessen had held a three-shot lead at the tournament's midway point after finishing his second round with an eagle, five birdies and one bogey on Saturday morning, as Friday's afternoon starters were forced to play catch-up following a weather-affected second day.
He stretched his advantage to five strokes early in the third round after picking up a birdie at the second to reach 12 under.
But the 28-year-old gave the shot back at the fourth, and even though he birdied the par-three seventh, a bogey on the 11th saw his lead reduced to a single stroke as the daylight began to disappear.
And with his playing partner Baldwin sending his approach shot at the 13th to within tap-in range before making a birdie there, Johannessen had company at the top.
Johannessen has a par putt waiting for him when the third round resumes.
England's Daniel Brown and Dutchman Joost Luiten set the clubhouse target at nine under to sit in a tie for third alongside Swede Jens Dantorp.
The second round had seen two holes-in-one on the 17th, with England's Dan Bradbury and South African Wynand Dingle both making aces.