England's World Cup defence in tatters after big defeat to South Africa
Klaasen made 109, despite being repeatedly troubled by cramp, as South Africa posted a colossal 399-7 -- the highest total conceded by England at this level.
England then collapsed to 68-6 and were 170-9, with exactly 28 overs to spare, when the match ended, with last man Reece Topley unable to bat following a hand injury suffered during South Africa's innings.
This crushing loss was England's heaviest ODI defeat following a 221-run reverse against Australia at Melbourne in 2002.
Klaasen received brilliant support from Marco Jansen in a sixth-wicket stand of 151 in just 77 balls.
Jansen finished on 75 not out - his maiden ODI fifty - having struck three fours and six sixes.
He then followed up with two early wickets in his more familiar role of left-arm quick.
Not even Ben Stokes, playing his first game of the tournament, could rescue England this time, with the talisman caught and bowled by Kagiso Rabada for just five.
England's third defeat in four games, including a shock loss to Afghanistan last time out, left them with a mountain to climb to reach the semi-finals.
By contrast, a resounding victory was just what South Africa needed after their stunning loss to the Netherlands, a non-Test nation.
Earlier, the big-hitting Klaasen struck a six and a four off successive deliveries from fast bowler Mark Wood to complete a 61-ball hundred.
He was eventually out when bowled by Gus Atkinson in the last over, having struck 12 fours and four sixes in total.
The Proteas ran riot as they scored 143 off the last 10 overs after losing the toss.
Topley took three wickets but conceded 88 runs in 8.5 overs, with express quick Wood going for 76 in a wicketless seven-overs.
England, who won the toss, had Quinton de Kock caught behind off just the second ball of the innings.
But opener Reeza Hendricks, who only received a late call-up after Proteas captain Temba Bavuma was ruled out through illness, made 85 and shared a second-wicket stand of 121 with Rassie van der Dussen (60).
Leg-spinner Adil Rashid removed both Van der Dussen and Hendricks, but he could only watch as Jansen smashed two successive sixes off Topley full-tosses.
England opener Jonny Bairstow fell for 10 before Jansen's fine day continued when he dismissed Joe Root and Dawid Malan to leave England 24-3.
After Stokes's exit, Gerald Coetzee took two wickets in three balls, England captain Jos Buttler edging to opposing wicketkeeper De Kock and Harry Brook lbw for 17 despite a despairing review.
South Africa's dominance was summed up when David Willey was brilliantly caught by a diving Rabada, running round from mid-off, to leave England 100-8.
Tailenders Atkinson (35) and Wood (43 not out) delayed the inevitable before the former was bowled by spinner Keshav Maharaj.