Andy Farrell's side prevailed with a Mack Hansen try, five points from the boot of captain Johnny Sexton and another three from the tee by Jack Crowley to stay top of Pool B on 14 points, four ahead of second-placed South Africa, with their 16th consecutive test win.
Cheslin Kolbe scored a try for the Springboks but Manie Libbok only had a penalty to show for his efforts, missing a conversion and another three pointer as Faf de Klerk also mi
Cheslin Kolbe scored a try for the Springboks but Manie Libbok only had a penalty to show for his efforts, missing a conversion and another three pointer as Faf de Klerk also missed a couple of long-range penalties, leaving his team beaten at the World Cup for the first time in nine matches.
Scotland and Tonga, who both lost their opening game in Pool B, face each other in Nice on Sunday.
"That was some atmosphere, if that's the sign of things to come, we're going to be looking forward to the next game, hopefully that pushes us along," Farrell said.
"It was two good teams going at it and not much between them. It's the next step on our journey, it's a pool stage win and that's what it is."
South Africa captain Siya Kolisi hailed his team's performance despite the loss.
"We would have loved to win but it was a great game, an intense game. Congrats to them, they played really well. They were able to hold the pressure in the first half and they got the try," he said.
"I am proud of the way we played. I think we left opportunities out there and they also did. It was a great test for us as a group."
South Africa came into the contest with a 7-1 split between forwards and backs on the bench and Ireland boldly looked to keep the ball in play as much as possible, going for the corner instead of kicking early penalties.
South Africa got onto the scoreboard first in a brutal start with a Libbok penalty as huge tackles and collisions drew oohs and aahs from the 78,542 crowd.
Ireland wasted chances with three disastrous lineouts but came close when Hugo Keenan ghosted past a tackler only to be brought down a couple of metres from the line.
'BOMB SQUAD' DEFUSED
Ireland looked to keep the ball in play, testing their opponents' rush defence, but made too many handling errors at first.
A long possession spell, however, was rewarded when Sexton danced his way into the South Africa defence, bringing the ball near the posts after a classic one-two with centre Robbie Henshaw before Hansen finished it off on the right flank after being set up by James Lowe.
It was the first try the Springboks had conceded at a World Cup since their semi-final against Wales in 2019.
South Africa made three changes to their forwards line, bringing in part of their 'bomb squad' early in the second half, and it immediately paid off as they won their scrum and Kolbe darted over to give his team the lead.
However, Sexton put the Irish back in front with a routine penalty and Libbok failed again from 40 metres after Ireland were sanctioned at the scrum.
With four minutes left, Ireland won another penalty in front of the posts, triggering a huge clamour from their supporters who were fired up by an ecstatic Hansen.
Crawley slotted it home and Ireland withstood a last South Africa charge to all but secure a quarter-final clash against the runners-up of Pool A - likely to be three-time champions New Zealand - while the Springboks could face hosts France.
