Davidson was in strong all round form in the 1961–62 Australian season, which was a purely domestic one. Against Victoria in Sydney, he scored 106 in a hard hitting innings with the tail. He made 58 of the 59 runs added in a last wicket partnership with Doug Ford, the other being a leg bye. The partnership lasted only 44 balls and Davidson managed to farm the strike and face 41 of these. The effort helped to set up a ten-wicket win. The following week against Western Australia in Perth, he made 108 after New South Wales had slumped to 6/38 to help the visitors recover to 218. New South Wales struggled in their second innings and Western Australia needed only 175 for victory. However, Davidson took his career best innings bowling figures of 7/31 to bowl out the hosts for 106 and seize a victory. In both matches against Queensland, Davidson took four quick wickets in the second innings to secure narrow victories after bold declarations. New South Wales won the Shield in that season with 64 of a maximum possible 80 points, playing aggressive cricket under Benaud. It was their ninth title in a row. Davidson was a key factor in the dominance, scoring 521 runs at 40.07 and taking 42 wickets at 13.62.