In 1983, Nzau was the first Kenyan to win in a world-class marathon when he won the 1983 Chicago Marathon. A year later, Nzau finished 7th overall in the men's marathon at the 1984 Summer Olympics. In addition to the marathon, Nzau finished 14th of 16 finishers in the men's 10,000 metres at the same competition. In 1990, Nzau won the inaugural Belgrade Marathon.