It was Merry's second goal of the tournament.
Barnett, who has won only seven international caps, was an outstanding last line as the Dutch -- missing only three players from this year's World up-winning team, strove for the winner late on.
The Netherlands and New Zealand lead pool A with four points each. China and Japan were squaring off this morning.
New Zealand play world No 5 China in their final pool game on Wednesday morning with a great chance of making the top four playoff spots.
''It was a really gutsy effort from the girls," Black Sticks captain Anita Punt said of a New Zealand display in which much of the match was given over to stout-hearted defence.
''We'll always take a draw against the Dutch."
Punt had high praise for Barnett's work.
''It's her first major tournament. She's awesome, she did great."
China and Japan drew their pool A game 1-1, leaving the Netherlands and New Zealand clear on four points each, with China and Japan on one point going into the final round of matches on Wednesday morning.