After some fine performances as a leg-spinning all-rounder for the Auckland Under-20 side in the 1964-65 Brabin Tournament (23 wickets at 10.47 in three matches), he was selected in the Test side just after his nineteenth birthday, against India in Calcutta, without having played a first-class match. He made a useful 43 in the second innings, coming in when New Zealand was struggling at 103 for 7 and helping the side avoid defeat. He toured England with the national team in 1965 but was unsuccessful with bat or ball, and did not play a Test.

He toured the West Indies in 1971-72 and played four Tests but without success. However, his fielding was outstanding: Henry Blofeld described the 1971-72 New Zealanders' fielding as "the most impressive I have ever seen from any side anywhere", and he singled out Vivian as "the best of all". He continued to play domestic cricket in New Zealand until 1978-79, but never played another Test.

His best first-class bowling figures were 5 for 59 for Auckland against Central Districts at Auckland in 1967-68. On a brief non-Test tour of Australia in 1969-70 he hit his highest first-class score (and first century) of 137 not out against Victoria in Melbourne, out of a New Zealand total of 220, having come to the crease at 22 for 4.^[5]

In 1981 Vivian established a company manufacturing synthetic turf for sports grounds. By 2007 its New Zealand factory was weaving 950,000 square metres of various kinds of turf a year.^[6]

• List of Auckland representative cricketers