"For a lot of the guys it was a proper taste of what Test cricket is about," said Bavuma of a hard-fought match which went into the fifth day.
"It's rare when you get to play for five days and it's also rare when the game is always in the balance. There were times when we were on top and times when Sri Lanka were getting the momentum on their side."
The win put South Africa on top of the World Test Championship table, which is based on average points gained.
South Africa can make certain of qualifying for the final at Lord's in England next June if they beat Pakistan in a two-match series which starts on December 26.
"The championship table looks good," said Bavuma during the post-match presentation. "We see ourselves at number one with two games to go. I don't know what the maths looks like but we're playing good cricket and we want it to continue."
Bavuma was named player of the series after scoring 327 runs in four innings, with a century and three fifties, but said other individuals in the team were making major contributions.
Three South Africans made centuries and three bowlers had five-wicket hauls, including left-arm spinner Keshav Maharaj, who took five for 76 to seal Monday's win.
"It's always a good sign when guys are putting in match-winning performances. It speaks to the hunger and desire amongst the team."
Sri Lankan captain Dhananjaya de Silva said his team had improved on their performance in Durban, where they were beaten by 233 runs after being blown away for 42 in the first innings.
"The guys fought hard but it was not good enough," said De Silva. "The bowling attack that South Africa had kept asking questions."
De Silva said Sri Lanka were improving in away Test matches. "We're getting better but we need to be 100 percent better in every department," he said.
Sri Lanka lost their remaining five wickets for 33 runs on Monday.
Their hopes of an upset win were extinguished when overnight batsmen De Silva and Kusal Mendis were dismissed inside the first 10 overs of the day.
De Silva and Mendis, the team's last recognised batsmen, resumed on 205 for five, still needing 143 runs to win.
Maharaj made the first breakthrough when Mendis edged a low catch to Aiden Markram at slip. He made 46 in a 97-run sixth wicket partnership with De Silva.
Kagiso Rabada then had De Silva caught behind for 50, exposing the Sri Lankan tail.
The last three wickets fell quickly with Maharaj claiming two more scalps and Marco Jansen finishing the match with his first ball of the day when Lahiru Kumara was caught off a wild slog.
