South Africa sent their hosts in to bat on Sunday, having already won the series with victories in the first two games, and England amassed 5-414 from their 50 overs as Bethell scored his maiden century in professional cricket with 110 in 82 balls and Root made 100 from 96 deliveries.
It was as though South Africa were batting on a different wicket as England then ran through their line-up, led by a fiery spell from Archer, whose pace and bounce were too much for the visitors as they were bowled out for 72, with captain Temba Bavuma unable to bat due to a calf strain.
The previous biggest winning margin was 317 by India against Sri Lanka in 2023 and while South Africa claimed the series, England have struck a psychological blow ahead of the teams' three-match Twenty20 International series that starts in Cardiff on Wednesday.
"It was the ultimate performance, we were awesome with the bat and put them under a lot of pressure. The bowling speaks for itself," England captain Harry Brook said.
"Jofra was bowling rockets, and to have that in your side alongside Brydon Carse and Jamie Overton is a frightening attack."
England opener Jamie Smith scored a brisk 62 from 48 balls before he was one of two wickets for spinner Keshav Maharaj (2-61).
Bethell and Root put on 182 in 144 deliveries for the third wicket as they flayed the bowling to all parts.
Bethell reached his first century in any form of professional cricket from 76 balls before the partnership was ended when he was stumped by wicketkeeper Ryan Rickelton from the bowling of Maharaj.
Jos Buttler kept the momentum going in the innings with an unbeaten 62 from 32 balls as England scored their fifth highest ODI score.
South Africa slipped to 4-7 in their reply with Archer bowling a lethal spell. He and spinner Adil Rashid (3-13) made light work of bowling South Africa out, though the visitors avoided their lowest ever score, the 69 they made against Australia in 1993.
"It was a poor showing from us, we will have a debrief to understand where it went wrong. Certain conversations will be had among the team," Bavuma said.
"Chasing 400-plus, there is no real formula behind it. In saying that, they put us under pressure, led by Jofra with the ball. We did not have answers to what they threw at us."
