Bethell's vibrant innings featured 13 fours and three sixes as the 21-year-old showed why England have been so keen to fast-track him in all formats.
Bethell easily surpassed his previous career-best score of 96 in a Test match against New Zealand in 2024.
Wreathed in smiles as he hugged Root to celebrate his milestone, Bethell had proved his point in emphatic fashion.
He admitted this week that he should have played more cricket over the domestic summer to stay in form.
Before this innings, Bethell had only faced 387 balls this summer compared to 1,480 in 2024.
Bethell, who will become England's youngest captain in an ODI series against Ireland later this month, made just six and five in his two Test innings against India.
He fell for one in the series opener against South Africa at Headingley but hit 58 from 40 balls at Lord's, having been moved up to number four, and maintained that form with an even more dynamic display on Sunday.
While Bethell represents England's future, the relentless Root is their present and the batsman's exquisitely-paced 100 brought him a 19th ODI century.
South Africa won by seven wickets in the opening match before a five-run victory at Lord's on Thursday.
South Africa won the toss and opted to bowl first as they chased a series clean sweep, but England made them pay with blistering stroke play.
Opener Jamie Smith survived an embarrassing drop by Matthew Breetzke to produce a dashing innings of 62 from 48 balls.
Bethell had reached 44 when he was dropped by Nandre Burger at mid-on.
Root strolled to his 44th ODI half-century and 172nd in all formats, but it was Bethell who stole the spotlight with his dazzling array of shots.
Unfurling a sumptuous drive to the boundary off Burger, Bethell was able to celebrate his maiden hundred in just 76 balls -- England's third fastest against South Africa in ODIs.
His partnership with Root had reached 182 by the time Bethell was stumped off Keshav Maharaj.
Aided by 62 not out in 32 balls from Jos Buttler, Root marched to his own century to ensure England didn't waste Bethell's barrage.