Anya Shrubsole took 3-35 as England restricted the Proteas to 196-9 from their 50 overs in Johannesburg.
Knight and Georgia Elwiss (61) put on 97 for the fifth wicket in the run chase to set up England's victory.
Despite the win, England stay fifth in the ICC Women's Championship standings, behind South Africa on net run rate.
Only the top four nations qualify automatically for the World Cup, which takes place in England in 2017.
England are currently second in the ICC's team rankings, but were fifth in the Championship table following last year's defeats by New Zealand and Australia.
They won the first ODI in Benoni by seven wickets, but South Africa took the second ODI, their first victory over England since 2004, at Centurion to level the series.
Knight won both the player of the match and player of the series awards.
"The last three matches have ebbed and flowed for us performance-wise," said England captain Charlotte Edwards.
"We have shown glimpses of what we are capable of with both bat and ball, but to be competitive with the best teams in the world we still need to be more consistent.
"We are starting to show signs of the positive, proactive and fearless cricket that we want to play, and I hope we can take this into the T20 series."
"It's nice to get over the line and, in the end, win quite convincingly," coach Mark Robinson, who secured victory in his first series in charge, told BBC Sport.
"I'm learning about the players, what they know and what they don't know. Half of them I met at the airport, three of them out here in South Africa.
"There's work in progress. Until today we haven't bowled very well, but now we've come to the party with the ball."
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England and South Africa now travel to Cape Town to play back-to-back T20 internationals on 18 and 19 February at Boland Park and Newlands Cricket Ground, before finishing the tour with the third and final T20 at the Wanderers in Johannesburg on 21 February.
The last two matches will be played as double-headers with the men's series.
Heather Knight hit an unbeaten 67 as England beat South Africa by five wickets at the Wanderers to complete a 2-1 one-day international series win.