Veteran pace bowler Kate Cross was injured in the first over of a rain-affected decider in Potchefstroom on Wednesday.
Cross was forced to leave the field after just five balls with a back injury in a potentially serious blow to Heather Knight's team ahead of their Australia tour.
England restricted South Africa to 8-233 despite Cross' absence and, after a delay due to wet weather and lightning, Beaumont's classy 65 not out alongside Amy Jones' crucial unbeaten 49 ensured the tourists chased down their revised target of 152 with four overs to spare.
Cross went down in her follow-through and walked off with pain in her back, with Alice Capsey forced to finish the over.
Capsey would go on to claim two wickets, including Marizanne Kapp for 38 but South Africa captain Laura Wolvaardt held the innings together with 61.
Sophie Ecclestone accounted for in-form Wolvaardt on her way to excellent figures of two for 26, with Charlie Dean also able to claim a two-wicket haul.
A lengthy delay followed the end of South Africa's innings with the threat of an abandonment a real possibility before the weather did relent to leave England with a tricky total of 152 from 23 overs.
It was made even harder when Maia Bouchier and Nat Sciver-Brunt were dismissed by Kapp from the first over of the tourists' chase.
When Knight and Danni Wyatt-Hodge quickly followed the duo back to the pavilion, England were in serious trouble on 4-63.
Beaumont kept her cool, though, and found a crucial ally in wicketkeeper Jones, with the pair able to find gaps in the field to keep the scoreboard ticking over.
Boundaries for each batter in the 16th over brought up milestones with Beaumont able to register her quickest every fifty off 35 balls and Jones becoming the second-fastest England woman to score 2000 ODI runs in terms of balls faced.
With the victory target within touching distance, Jones hit two fours before Beaumont smashed a boundary through fine leg to help England clinch a 2-1 ODI series win ahead of next week's one-off Test.
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