New Zealand's opening bowlers took some heavy stick from the Afghan batsmen. New Zealand's opening batsman Martin Guptill was dismissed for a golden duck.
The spirited Afghanistan lineup created trouble for the 2015 Cricket World Cup finalist at times on Somerset's Country Ground but ultimately weren't quite a match.
A seven-wicket victory on Saturday gave New Zealand three wins from three games to start the tournament, and consigned Afghanistan to its third straight loss.
Compounding woes for cricket's newest top-level team, star spinner Rashid Khan was hit on the helmet while he was batting and couldn't contribute for an Afghan bowling attack trying to defend a small total.
For New Zealand it was the bowling depth that proved crucial, with change bowlers Jimmy Neesham (5-31) and Lockie Ferguson (4-37) reining in the Afghan innings after Hazrat Zazai (34) and Noor Ali Zadran (31) got away to a flyer.
The New Zealand chase was less dramatic, despite the first-ball loss of Guptill to Aftab Alam's first ball of the tournament.
Kane Williams led the way with an unbeaten 79, including an 89-run third-wicket partnership with ex-captain Ross Taylor (48) as New Zealand reached 173-3 in the 33rd over.
Afghanistan was up against it after losing the toss and being sent in to bat in overcast conditions on a green-tinged pitch, yet the openers plundered 12 off the first over and raced to 66 in the 11th over before the innings unraveled.
Neesham struck to remove Zazai, Ferguson dismissed Noor Ali two balls later and Neesham snared two more wickets as Afghanistan lost 4-4 in 20 balls. It was reminiscent of Afghan innings in losses to defending champion Australia and 1996 champion Sri Lanka earlier in the tournament, as wickets fell in clusters.
Two rain delays didn't help them, but Hashmatullah Shahidi dug in with 59 to lift Afghanistan to 172 in 41.1 overs.
Neesham claimed two more wickets around the rain delays and Ferguson, after bowling three consecutive maiden overs to tie the Afghan run-rate down, returned to get three of the last four.
Two of those were crucial. He finished Hashmatullah's defiant 99-ball stand to end the innings after knocking Rashid out of the game — the Afghan tailender ducked into a short ball and had to undergo assessment for concussion.
Rashid didn't come back to the field, with Afghanistan's team doctor deciding it was safer for the young spinner to rest.
Alam was one of three changes to the lineup and earned his place immediately by having dangerous Kiwi opener Guptill caught to start the reply.
He also had Colin Munro (22) caught in the deep and bowled Taylor with a full, slower ball to return 3-45.
After three games in 10 days, Afghanistan gets a week off before taking on South Africa in Cardiff.
New Zealand's degree of difficulty increases markedly with a game against 2011 champion India in Nottingham.
