The Springboks looked on the verge of defeat as England's kicking game worked wonders at a rainy and windy Stade de France, but a late surge through RG Snyman's try and Pollard's kick with less than three minutes left gave them a scrappy win.
The two super powers of the sport will meet in the final for the second time, after South Africa triumphed on home soil in 1995 in their first appearance at the tournament.
For most of the match, however, it looked as if it would be 2019 runners-up England returning to the final. On a rainy Paris night, England played a perfect tactical game, kicking accurately, chasing hard and forcing South Africa into errors.
Coach Steve Borthwick had promised he had a plan to unsettle the world champions but there was nothing radical about their approach as they kicked relentlessly in the rain and outplayed the Springboks in the air.
England forced South Africa into the sort of errors they avoided in their epic quarter-final win over France.
England’s control and accurate pressure earned Owen Farrell two early penalty opportunities, both of which he slotted for a 6-0 lead.
After 15 minutes South Africa won a kickable penalty but, lacking faith in Manie Libbok, they kicked for the corner and were turned over and they did the same a minute later, and lost possession again.
Libbok did slot one over but he looked off the pace and was taken off after 31 minutes, replaced by Pollard, who soon landed a penalty.
England, however, maintained their disciplined approach, gaining ground from their deep kicking, and another Farrell penalty gave them a deserved 12-6 halftime lead.
There were more changes for South Africa in the first five minutes of the second half as Faf de Klerk and Willie Le Roux came into the backline and they lost inspirational lock Eben Etzebeth.
The champions still struggled to get any sort of continuity and England stretched their lead to 15-6 with a brilliant 47- metre Farrell drop goal.
HEAVY PRICE
With half an hour to go all the South African replacements were on as their coaches desperately sought to find a foothold, though England were to pay a heavy price for their failure to turn their dominance into any more points.
The Springboks had barely been our of their half before a superb touchfinder by Pollard enabled Snyman to charge over for the first try of the match.
Pollard converted to close to within two points 10 minutes from time and they were awarded a scrum penalty on halfway with three minutes to go.
Pollard, called up to the squad midway through the tournament, slotted it with the minimum of fuss.
It was the first time South Africa had led and they then defended England’s final assaults until a knock-on ended the challenge.
England relied on the boot of Farrell, who kicked four penalties and a long-range drop goal, but their limits eventually showed.
They will meet Argentina next Friday in the third-place playoff at the Stade de France.
