With Ben Youngs and skipper Chris Robshaw ruled out through injury, Care and Haskell earn their chances back in the side - while prop Corbisiero is preferred to Joe Marler and Palmer replaces Botha in the second row.
There are also first starts for Thomas Waldrom and Alex Goode after they impressed off the bench in the second-Test loss to Johannesburg.
Waldrom replaces the out-of-sorts Ben Morgan at No.8, while the impressive Goode comes in at full-back with Ben Foden switching back to the wing in place of the benched David Strettle.
England coach Stuart Lancaster said: "I am really pleased for Alex. He has worked hard in training and has been pushing Mike Brown and Ben Foden close so we are looking forward to him bringing his footballing skills to this Test.
"Danny Care likewise has bided his time in a very competitive position, knuckled down and deserves his chance, as has James Haskell, who has played this season for the Highlanders at No.7.
"We felt that the pack got some momentum in the second half last week so we have gone for Alex and Tom but I am sure Joe Marler and Mo Botha can make an impact from the bench.
"The guys did the shirt proud in Potchefstroom on Tuesday and I have no doubt that the 22 involved on Saturday will rise to this final challenge as we look to end this almost 12-month season on a high."
England: 15 A Goode, 14 C Ashton, 13 J Joseph, 12 M Tuilagi, 11 B Foden, 10 T Flood, 9 D Care, 1 A Corbisiero, 2 D Hartley (capt), 3 D Cole, 4 T Palmer, 5 G Parling, 6 T Johnson, 7 J Haskell, 8 T Waldrom.Replacements: 16 L Mears, 17 J Marler, 18 M Botha, 19 P Dowson, 20 L Dickson, 21 O Farrell, 22 B Barritt.
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