England trio Issy Wong, Lauren Bell and Alice Davidson-Richards all took debut wickets, but Kapp led a South African resurgence as they recovered from 4-45 when she came to the crease to reach 276 when she was ninth out.
Kapp was one of only two South Africans to go into the game in Somerset with a Test cap and looked to dominate from the start, playing expertly as she made 150 from 212 deliveries.
However, she ran out of batting partners, with Anneke Bosch the next highest scorer with 30, despite batting getting easier throughout the day, England having won the toss and elected to bowl.
It was a new-look England side featuring four debutants, but the youngsters held their own against South Africa, who were playing their first Test match since 2014.
England bowled well at the start of the day, with Kate Cross the pick of the bowlers after being promoted to opening the bowling following the international retirement of Anya Shrubsole and Katherine Brunt's decision to focus on white-ball cricket.
Cross finished with figures of four for 63, including the wicket of captain Sune Luus.
Kapp was best-supported by Bosh and the pair put on 72 for the sixth wicket before Bosch was caught, handing England off-spinner Sophie Ecclestone her first wicket of the Test.
The centurion eventually fell to Bell just after bringing up her 150 when she looked to play down the ground, as she had so expertly throughout her innings, but Tammy Beaumont took a high diving catch at mid off.
In her only other Test match, against India in 2014, Kapp made 19 and 0 and admitted: "When I first started I was very nervous, especially that the first Test match was an absolute nightmare.
"But I think you just have to focus a bit longer. It's still cricket."
I thought Kapp was absolutely outstanding," said Cross. "To say that we've not played much Test cricket, I mean it's probably eight years since they've played.
"Just how she manipulated the field, how she manoeuvred others, how she played us, how she managed to keep the strike, it just was like she's played Test cricket for years. We needed something special to get her out."
After South Africa were dismissed there was insufficient time for England to embark on their innings.
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