Stokes, however, suffered a knee injury - having had surgery past year - at Headingley and is now set to have a scan.
Press Association Sport understands the all-rounder was due to have a scan in Southampton on Thursday evening on the same left knee that required surgery to address a cartilage tear past year.
The success enhanced England's status as favourites for the Champions Trophy, which starts on 1 June, and boosted hopes of Morgan leading the country to its maiden piece of worldwide 50-over silverware.
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.
Ali, who ended England's innings with a six off Chris Morris, was named man-of-the-match after also taking two wickets with his off-spin.
A magnificent century from England skipper Eoin Morgan sent England on their way to a comprehensive 72-run win over top-ranked South Africa at Headingley.
"A couple of days with ice on it will do him good".
But before then, they still have two ODIs against the Proteas, with Saturday's match at Southampton followed by a series finale at Lord's on Monday.
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Zverev, who is regarded as one of the most gifted players on tour, broke his racket during the fourth set. The latter refused a post-match hand shake with Klizan and accused his opponent of faking injury .
South Africa have defeated teams like Australia and Sri Lanka with some ease, and such records will give them the self-belief to crush opponents, including England in this series.
"We couldn't get a partnership going [with the bat] and at the end of the day we were outplayed".
South Africa found their own stable pair at the top in Hashim Amla and Faf du Plessis but like Hales and Root, the duo fell in quick succession to leave de Villiers with too much work to do.
England and South Africa have received reassurances over security measures for their one-day global series, which starts at Headingley on Wednesday, following Monday's bombing in Manchester.
"It depends where you play", De Villiers said of the potential high scores.
Morgan, however, went to his hundred when he hooked fast bowler Kagiso Rabada over long leg for six.
If England were hoping to crank up the pressure with the new ball Amla quickly disabused them of the notion, laying into Mark Wood with some elegant strokes.
When Jos Buttler was dismissed, England were struggling at 198 for 5 but they scored 102 runs in the last ten overs, an onslaught that consisted of seven sixes and four boundaries.
South Africa were fined after the match for maintaining a slow over-rate. JP Duminy got to 15 before hoisting a poor ball from Rashid down Chris Woakes' throat.