Taylor smashed eight fours and a six in his 116 off the same number of deliveries as England posted a formidable 368 for seven in their 50 overs having won the toss and elected to bat.
The home side never looked like reaching that target and were all out for 205 from 30.5 overs.
The magnificent Taylor was ably supported by a cameo from Jonny Bairstow (58 from 30 balls), a remarkable innings that included no fours but six massive sixes from the Yorshireman.
Chris Jordan also weighed in with a lively unbeaten 33 from 14 balls, while captain Eoin Morgan scored 41 at a run-a-ball.
South Africa A managed to score at a rapid rate but lost wickets at regular intervals, with Theunis de Bruyn (73 not out) providing some lone resistance.
There were three wickets each for Reece Topley (3-38), Jordan (3-48) and Adil Rashid (3-55).
The most economical of the England bowlers was David Willey, who returned figures of 1-23 in his five overs.
The first of five One-Day Internationals against South Africa will be played in Bloemfontein on Wednesday.
(Editing by Martyn Herman)
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