Morkel smashed his 43 off 20 balls. He hit three fours and four sixes, three of them consecutively off leg-spinner Chris Schofield.
Number seven batsman Morkel came to the crease in the 15th over after South Africa had slumped to 91 for five, and six balls later they were 94 for six.
Pace bowler Stuart Broad led the England attack with his return of three for 37.
England bowled with discipline but did themselves no favours by dropping five catches.