Burgess made his first-class debut for a New Zealand Under-23 XI against Auckland in 1963–64 at the age of 19. He played his first matches in the Plunket Shield for Auckland in 1966–67, scoring 270 runs at 33.75 in six matches. It was enough to secure his selection for the short non-Test tour of Australia in 1967–68, and the four Tests against India that followed in New Zealand, when he scored three fifties and was the second-highest-scoring New Zealander with 271 runs at 33.87.