Similarly to their opener with France, the Republic of Ireland made a strong start in Utrecht but could not make the most of their early opportunities.
McCabe's deep corner was headed back across goal by Caitlin Hayes and Wilms had to get a touch to divert the ball around the post with her knee.
The Brighton defender had a great chance moments later when Kyra Carusa hooked the ball across goal and Hayes, still up from the previous attack, could not head her effort on target.
The Netherlands started to grow into the game from there. Wieke Kaptein dragged a shot wide from range before Courtney Brosnan had to be alert to claw the ball away from the feet of Beerenstyn when the Wolfsburg forward looked like she would tuck the ball away.
But the hosts took a deserved lead when Wilms played a superb low ball across goal and Beerensteyn got in ahead of Aoife Mannion to touch home.
Beerenstyn, who was getting all sorts of space in behind the defence, should have added a second at the end of the half but Brosnan made herself big to keep the forward out.
However, the Republic of Ireland drew level five minutes after the restart when Hayes was caught by Kop when the Dutch keeper tried to punch the ball clear and McCabe emphatically dispatched the penalty.
Beerensteyn fired over from close range and Romee Leuchter directed a free-kick straight at Brosnan as the hosts looked for an immediate response, and Manchester City's Vivienne Miedema had a gilt-edged chance when she fired over from Wilms' cut back from the edge of the area.
Megan Connolly and McCabe had long range efforts for the Irish but, in an outcome that mirrored the heartbreak of the game with France on Tuesday, there was late drama to come.
Brosnan went to punch Esmee Brugts's corner but the ball fell kindly to Beerensteyn, who beat Connolly to the crucial touch and she was able to find the back of the net with eight minutes left.
The Irish pushed for a late equaliser but came up just short of securing a famous point against the 2017 European champions.