Match referee David Boon adjudged that the Kiwis had bowled one over short of their target after time allowances were taken into consideration.
Skipper Kane Williamson pleaded guilty and was fined 20% of his match fees while his team mates were handed 10% fines in accordance with article 2.22 of the ICC's Code of Conduct, the governing body said in a statement.
"If New Zealand commit another minor over-rate breach during the tournament with Williamson in the side, it will be deemed a second offence by him and he will face a suspension," the ICC statement added.
New Zealand moved to the brink of securing a spot in the World Cup semi-finals with a thrilling five-run victory over West Indies.
New Zealand take on Pakistan at Edgbaston on Wednesday.
(Reporting by Shubham Kalia in Bengaluru, editing by Pritha Sarkar)