When Dexter's Englishmen toured Australia in 1962–63, McKenzie was promoted to share the new ball with Davidson. Playing in all five Tests, he did not trouble the batsmen to the same extent as his partner, taking 20 wickets for 30.95. He was noted for his ability to contain the opposition by bowling long spells. Davidson retired at the end of the series and McKenzie became the pace spearhead when South Africa toured in 1963–64. He was Australia's leading bowler with 16 wickets at 43.06. In the Third Test in Sydney, he hit his highest Test score of 76.