Phillips was the top scorer with 71 off 80 balls and put on 144 runs for the fifth wicket with Latham (68) to rescue the Black Caps from a precarious 110-4 as they posted 288-6.
New Zealand curtailed Afghanistan, which was coming off a surprising 69-run win over England, to 139 all out in 34.4 overs and registered another big victory in the competition to boost its net run rate.
The Black Caps are in first place on a maximum eight points, with India — with three straight victories — the only other unbeaten team.
Rahmanullah Gurbaz, Ibrahim Zadran, Rahmat Shah, Hashmatullah Shahidi (c), Azmatullah Omarzai, Mohammad Nabi, Ikram Alikhil (wk), Rashid Khan, Mujeeb Ur Rahman, Naveen-ul-Haq, Fazalhaq Farooqi
Devon Conway, Will Young, Rachin Ravindra, Daryl Mitchell, Tom Latham (c & wk), Glenn Phillips, Mark Chapman, Mitchell Santner, Matt Henry, Lockie Ferguson, Trent Boult