Second-half tries from flanker Pieter-Steph du Toit and wing Kurt-Lee Arendse eased the Springboks to an important win in Marseille, with world No 1 Ireland also in the group and only two teams advancing to the quarterfinals.
"This was always going to be a slippery one; they (Scotland) are the No 5 team in the world and they deserve that ranking," South Africa coach Jacques Nienaber told reporters.
"They have the ability to beat anyone on the day. For us it is the first step in the right direction."
The Boks lost Etzebeth to a shoulder injury after 26 minutes, a potentially huge blow for a player who is so instrumental to their powerful pack.
"He will be assessed on Monday, at this stage we have no idea how serious, or not, it is," Nienaber said.
Nienaber was South Africa’s defence coach when they won the World Cup in 2019 and hailed the effort of his side to keep at bay a Scotland side who have gained a reputation for the efficiency of their attack.
"They are a team that play with great speed and have got good innovation in terms of how they attack," Nienaber said.
"We had to be really sharp in terms of cutting off their options. They can create something out of nothing.
"There was a lot of hard work off the field (in the build-up to the game), but also on the field to keep them at bay. It took a lot."
South Africa face minnows Romania in their second game next Sunday and Nienaber said they were focusing entirely on that fixture, rather than looking ahead to a potential pool decider with Ireland on 23 September.
"Our next focus is Romania only. We won’t even think about Ireland. We also need to fix the things we got wrong tonight."
