The hosts enjoyed a bright start and threatened on the quarter-hour mark when a cross from the right flashed across goal, but Vito Wormgoor was on hand to clear away the danger.
In the 50th minute, the hosts were awarded a penalty following Wormgoor's foul in the box, but Nick van der Velden's effort from the spot was saved.
There was no respite when the same thing happened two minutes later, with Timothy Derijck being judged to have handled in the box. Tjaronn Chery lined up and blasted home from 12 yards to put his side ahead.
Just when it seemed as though Groningen would hang onto all three points, one last surge into the home box saw Aaron Meijers lash a strike towards goal, which deflected off Houtkoop and into the net.
The result keeps Groningen 11th in the Eredivisie table, with now Den Haag in 14th.