They were subsequently bowled out for 153 in only 31.1 overs, before the tourists sealed victory in 28.5 either side of the lunch break in the third and final Royal London Series match.
Jonny Bairstow's brawny fifty: Bairstow, replacing Ben Stokes in the playing XI, came in as early as fourth over.With England lurking at 20 for 6, Bairstow took upon himself to resurrect the innings. But medium-pacer Jake Ball conceded only three runs off his last four deliveries, and Wood gave up only four singles in a tense last over.
"Credit to South Africa", he said.
Bairstow was stumped off spinner Kershav Maharaj and England still had just under 19 overs to bat when Steven Finn chipped the ball to midwicket and was the last man out.
In 2004, they reduced the West Indies to 147 for eight chasing 218 only to suffer a two-wicket defeat.
Morgan said he did not expect to encounter a similarly bowler-friendly pitch at any of the three Champions Trophy venues - The Oval, Edgbaston and Cardiff.
South Africa had moved relatively comfortably to 56 without loss when Stokes struck. In company of a returning Quinton de Kock from injury, the duo will be one of the most unsafe opening pair in the tournament.
England and South Africa play a third ODI at Lord's on Monday, after which both participate in the Champions Trophy.
Roy endured a miserable series against South Africa, scoring just 13 runs in three innings.
AB de Villiers has taken a break from Test cricket to focus on limited-overs cricket, and appears determined to lead South Africa to their first piece of limited-overs silverware since the 1998 ICC KnockOut Trophy.
Morgan added: "I'm not anxious".
Rabada was the pick of the bowlers with four wickets, while Parnell and Maharaj snapped up three wickets apiece. "Batting and running around the field and everything like that is fine". Then the doctors, physios, strength and conditioning coaches have a clear idea of what we can do to counteract it and maybe take the problem away, which is obviously what I want and what the medical staff wants. Pretorius was swung crisply down the ground for a one-bounce four, then Phehlukwayo mowed over deep midwicket for six; when Morris returned, he was deposited into the Shane Warne Stand off an even more towering blow.
England were faltering at 80 for three when Stokes came into bat.
Rabada had out-of-form Jason Roy caught in the slips by Amla in the opening over and Joe Root, Morgan and Jos Buttler followed in quick succession to catches.
The victory puts England in place to complete a bilateral whitewash over South Africa for the first time in 26 years.
If that trio return, it appears Bairstow would be favourite to miss out again.