Inglis matched the 102 he scored against Sri Lanka on his test debut last year as he batted superbly with Alex Carey (80) to put Australia in command of the match.
Leeds-born Inglis, 31, came into the side when experienced batter Steve Smith pulled out on the morning of the first day with a neck injury.
"It wasn't ideal preparation (for the game), but Steve had been dealing with his neck issue for a while, so in my mind I was always preparing to play, just in case," Inglis told reporters.
"He came down to the ground early, had a hit and didn't feel comfortable enough to play. I found out I was in the team once we got to the ground."
South Africa scored 329 in their first innings and Australia managed 429 in reply, led largely by Inglis’ 102.
"When I got out there, I realised it was a really good wicket, so the most important thing was making sure we got a lead," he said.
"I'm still a bit disappointed we didn't get more runs this morning.
"If Kez (Carey) and I could have added another 50, that would have been really nice.
"We knew how good the wicket was and felt we needed a big total."
South Africa finished the day on 140 for four in their second innings, only 40 runs ahead with six wickets remaining. Australia grabbed the key wickets of Marques Ackerman (62) and Temba Bavuma (35) late in the final session.
"It was really satisfying. I thought we controlled the tempo well in that last session," Inglis said.
"They put together a good partnership and were batting well, but they weren't really getting away from us.
"Gaz (spinner Nathan Lyon) bowled brilliantly and looked threatening the whole time. When you work hard for a couple of hours and finally get the rewards right at the end, it's really satisfying."
Inglis said chasing anything over 200 could be tricky batting last.
"I'm not sure of a total (to chase). You don't want them getting too many more than maybe 200 or so (ahead)," he added.
