Lily Owsley gave GB the lead from close range but Kitty van Male equalised just before the break.
Helen Richardson-Walsh got the winner when she scored her 39th international goal after Giselle Ansley had a shot parried.
The teams will play the second Test on Thursday.
"It was a slightly disjointed but winning performance," said GB head coach Danny Kerry. "We can be better with the ball but we were defensively solid which won us the game.
"We're looking forward to 48 hours time when I feel we will have made some good adjustments to our game."
Great Britain beat Olympic and world champions Netherlands 2-1 in Amsterdam in the first of a two-match Test series.