Alastair Cook’s side won the toss and immediately tore into the Proteas with Stuart Broad and James Tredwell each taking three wickets as South Africa were skittled out for 175 with more than 11 overs remaining of their innings.
Captain Cook fell early in England’s reply, but Jonathan Trott compiled a masterful 82 not out to lead the hosts to victory with 75 balls remaining in what was a one-sided contest in the first semi-final to move to within one win of their first global one-day international trophy.
South Africa, who were the favourites heading into the tournament but limped through the group stage, have now bowed out in eight major international last-four clashes having only won one.
England, who came into the tournament as outsiders having lost a home one-day series to New Zealand, will face either Sri Lanka or world champions India in the final at Edgbaston on Sunday, with the two sides set to lock horns in Cardiff on Thursday.
Trott took control of England's run-chase on a gloriously sunny day in London after Cook departed for six to fast bowler Chris Morris and Ian Bell went for 20, and Joe Root was the perfect partner for the unflappable number three with 48 before he was bowled by JP Duminy attempting an audacious sweep.
Eoin Morgan came in and blasted two boundaries before Trott, fittingly, was able to finish the match with a sumptuous cover drive - his 11th boundary of the day - as England closed out a convincing victory against a South Africa side who again were unable to perform on the big stage at a major tournament.
The damage was done early in the day as the consistently excellent Anderson took two wickets for just 14 runs from his eight overs, the first of which saw opener Colin Ingram fall for a five-ball duck.
After making an inauspicious start to the match, South Africa continued to struggle as the key man Hashim Amla edged behind off Steve Finn for just one, and it was left to Robin Peterson and Faf du Plessis to repair the early damage.
The pair put on 41 for the third wicket before Anderson claimed a second lbw dismissal to send Peterson back to the pavilion for 30, and the Proteas' woes were compounded as man-of-the-match Tredwell entered the fray.
The underrated off spinner, replacing Graeme Swann, again distinguished himself with three for 19 off his seven overs, and the first of his scalps was the dangerous du Plessis, who could only muster 26 after making a bright start.
Captain AB de Villiers simply had to bail his side out, but the scorecard looked even worse as he was caught behind by wicketkeeper Jos Buttler - who took six catches in the innings - with Broad taking the crucial wicket for the hosts to leave South Africa reeling on 50 for four.
Duminy could only add three runs to the board before he was outfoxed by the inspired Tredwell, and when Ryan McLaren was run out by Trott the match was heading towards a very anti-climactic early conclusion.
Morris was caught behind off Tredwell for just three, but that brought together David Miller and Rory Kleinveldt, who put on 95 with 56 not out and 43 respectively to highlight the failings of the frontline batsmen on a perfectly good wicket.
Broad mopped up the tail with Buttler combining for the wickets of Kleinveldt and Lonwabo Tsotsobe, and it was always looked as though England should cruise to their target. As it was, Trott managed to make the task easier than it actually was, with a typically composed and valuable contribution for Cook's side.
England now await the winner of the second semi-final between Sri Lanka and India, who take on each other in Cardiff, with the final at Edgbaston on Sunday. The hosts were the joint-favourites, along with South Africa, coming into the tournament, and it would be foolish to discount their chances in Birmingham.