The second singles match, between Scholtz and Monaco No 1 Benjamin Balleret, was suspended in the second set due to bad light. The South African clinched the first set 7-5 and was trailing 1-3 in the second set.
Earlier, veteran Rik de Voest was stunned by Monaco debutant Romain Arneodo in the opening match after the start was delayed by two hours because of rain.
De Voest put up a strong fight to draw level twice, having lost the first and third sets, but he was narrowly edged as the tourists grabbed a 1-0 lead.
Arneodo held his nerve to secure a thrilling 7-5, 3-6, 7-5, 5-7, 6-4 victory in a five-set encounter that lasted four-and-a-half hours.
“I’m obviously disappointed. I wanted to do well and get South Africa off to a good start,” De Voest said.
“There were a few chances in the first set that I didn’t take and he got better as the match went on.
“It was not my best match, but I felt I fought hard to the end.”
Arneodo, ranked 358 places below the South African in the ATP singles list, was delighted with his surprise win, forcing the hosts on the back foot early in the tie.
“I feel so good and I’m so proud of what I’ve done today,” Arneodo said.
“It’s the first time I’ve played a five-set match, and it’s the first time I’ve played Davis Cup.
“I had some physical problems with cramps last year, so to win this match against a player with his experience means a lot to me.”