The Boks led from the moment Kurt-Lee Arendse scored the first of their three tries in the third minute, but they edged their way to victory in a tense second half in which Ireland threatened to snatch victory as the clock counted down.
“Overall, the goal was achieved but it was far from a perfect performance,” said Erasmus.
“Ireland are a team we’ve had zero success against since (we took over in) 2018 and the next worst record is against New Zealand – which is a 50% record – and they’ve really had our number.
“And there were instances where they came back so strongly and if they didn’t have one or two big injuries the game would have been much tighter.
“I wouldn’t say it’s a monkey off our back but it’s a really good competitive opponent, who are number two in the world, and any day they can step up and beat you and be number one.”
Bok captain Siya Kolisi said he was pleased with the result but cautioned that the series remained very much alive.
“Of course, this game was very important for us,” he said. "We haven’t beaten them since 2016, so it was special for our confidence. But the job is not done yet. We want to win the series and we know they are going to come back harder.
“Even in the game today it looked like we were going to pull away but they kept coming back so we know it is going to be another proper Test in Durban.”
The Springboks also scored through a try for wing Cheslin Kolbe and were awarded a penalty try from a dominant scrum, while flyhalf Handre Pollard kicked two conversions and two penalty goals.
But the Boks also created several other openings with a more expansive gameplan.
Erasmus said: “I hope you can see we’re trying to develop our attacking game with the foundation that Felix (Jones) laid. With Tony (Brown) we’re trying to step up a little in certain areas and with that comes mistakes and lack of cohesion.
“But saying that Ireland are not No 2 in the world for nothing and their defensive system is really sound. It was a very stop-start game, there was a two-minute delay here with either an injury or someone getting treated – it was no one’s fault – but for both teams it hampered momentum.”
Kolisi added: “I’m really enjoying the way coach Tony is getting the team to attack as a group so I really enjoyed getting the ball in my hand today. We’re going to get better each week; we are still learning what coach Tony wants us to do but it is only going to get better.”
Erasmus said: “Ireland will work out what we tried to do tonight, and we’re going to try and work out what they did because they also scored three tries.”
“Next week I’ll expect the same from them – they’ll never give up and they’ll try to be more dominant. They’ll be more settled in the second test – they were disrupted with injuries – but even when Cheslin scored his try [to make it 20-8] to put us in a strong position, they didn’t give up and even to the last second we were nervy about the game.”
The win was South Africa’s first in four attempts since 2016 against Ireland. The second test takes place at Hollywoodbets Kings Park on Saturday (kick-off 17h00).