Borren made his highest T20 score of 49 and Cooper scored 40 not out during their invaluable 60-run stand for the fourth wicket off just 35 balls.
The pairing ensured the Netherlands recorded a testing chase score after they were sent into bat at Zahur Ahmed Chowdhury stadium.
Borren hit seven boundaries and a six off 35 balls to improve on his previous best T20 score of 38 not out that he made against Afghanistan at Sharjah last year.
Cooper knocked two sixes and four boundaries off 23 balls to help his team add 43 in the last five overs.
The Netherlands were off to a steady 34-run start with opener Stephan Myburgh hitting a boundary and a six before he holed out to paceman Trent Boult, who replaced Tim Southee in the team.
New Zealand also brought in allrounder Jimmy Neesham for Colin Munro from the line-up which beat England on Saturday.
Michael Swart made a run-a-ball 26.
The Netherlands, unchanged from the side out for the lowest-ever T20 score of 39 against Sri Lanka in their first game here, need a win to stay in the tournament.
The top two teams from both groups will qualify for the semi-finals.
India have already qualified for the last four from Group Two.