But South Africa, who have not beaten England in a Test for 13 years, took advantage of a sluggish start by the hosts at the University of Bath to open up a 17-13 lead during the second quarter.
Substitutions from head coach Anna Mayes midway through the quarter made the difference for England, who are ranked third in the world, three above places above the Proteas.
Jo Harten was replaced, with Cookey moving to goal shooter and Kadeen Corbin coming on at goal attack, and within minutes England had moved into a 21-19 lead.
At the start of the second half Corbin moved to goal shooter, with Cookey returning to goal attack, and only three minutes later the hosts had extended their lead to 29-23.
South Africa shooter Melissa Myburgh looked lively inside the semi-circle against the England defensive pair of Eboni Beckford Chambers and Stacey Francis.
But the visitors failed to capitalise on their possession and the hosts' superior experience saw them pull well clear by the final whistle, although the scoreline did not reflect how tight the game had been at times.
England coach Mayes admitted: "Some of our great play was spoilt by ill discipline. I'm pleased with the people who came off the bench and made an immediate impact and I'm pleased with Mia Ritchie who really opened up the attack. It's a great asset to us that we can switch up attack."
Listen to live commentary of the final two England v South Africa Tests at bbc.co.uk/sport
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