Nicol brought up his second century from only five one-day international appearances and the fifth-highest innings by a New Zealander in 50-overs matches, batting until the 49th over to anchor New Zealand's innings of 372-6.
The total was New Zealand's third-highest in one-day internationals after its 402-2 against Ireland in 2008 and 397-5 against Zimbabwe in 2005.
Oram chipped in 59 from 28 balls, batting at his highest position in the New Zealand order in 10 years, then took 3-29 as Zimbabwe was held to 231-8 in reply.