Earlier, Morgan's 107 - his 10th ODI hundred for England - was the cornerstone of the hosts' 339 for six.
Yet Morgan may decide not to risk Stokes either at Southampton or in the final match of the series, at Lord's two days later. If they do so, it would be England's first major global title in the 50-over game. Rabada over-stepped the frontline on three occasions, which gifted Englandopener Alex Hales the opportunity to get his innings underway with a couple of free hits.
The last of them, a crisp blow past point off Tahir, took him to a spirited half-century in just 44 balls.
But Morgan twice lofted Phehlukwayo for six.
Phehlukwayo then undid Root (37) with a bouncer the local hero mishooked to Amla.
Stokes, in his first England match since his most valuable player-winning stint in the lucrative Indian Premier League competition, came back on later Wednesday but did not add to his tally of two overs.
Faf du Plessis, who had batted beautifully for his 67 in a 112 run partnership with Amla, quickly followed after edging Liam Plunkett with keeper Jos Buttler safely pocketing. At that stage England were 198/5.
"I don't think as sports people we should allow ourselves to be held ransom, otherwise you won't have world events, you won't have touring teams".
AB de Villiers' had stifled momentum with judicious use of spin duo Imran Tahir and JP Duminy but, after the pair's first 46 balls failed to leak a single boundary, Morgan took the bull by the horns and produced three in the space of six deliveries.
Eoin Morgan believes this is the strongest England white ball side he has been involved in - and says he enjoys the "luxury" of having to select a starting team.
Morris claimed 2/61 and owned the only maiden of the innings.
"[Stokes injury?] I don't know, it's in his knee, no significant swelling".
But Amla again proved a thorn in England's side with a typically elegant near run-a-ball 73.
AB, batting at 4, fought a lone battle scoring a 38 ball 45. David Miller offered up a carbon copy, hooking Woakes to Ben Stokes on the fence.
Eventually, the asking rate became too steep and de Villiers was forced to go big, resulting in his dismissal.
Morgan, however, went to his hundred when he hooked fast bowler Kagiso Rabada over long leg for six. Andile Phehlukwayo survived an lbw appeal, but then missed an attempted sweep of Rashid and was bowled.
South Africa has won all their last 6 bilateral series and the record to stay unbeaten will be on the line in the do-or-die 2nd ODI at the Rose Bowl on Saturday.