Invited to bat in the inconsequential group tie, the Dutch openers had to wait for more than two and a half hours to take to the field with the rain-affected game reduced to 6-overs-a-side.
Left-hander Stephen Myburgh struck an 18-ball 27 to help Netherlands post 59 for five and the bowlers did well to defend the total.
Medium-pacer Van Meekeren (4-11 from 2 overs) tore into the Irish batting getting good support from left-arm spinner Roelof van der Merwe, who picked up two scalps, to restrict Ireland to 47 for seven.
“It’s special, I’m not sure if it’s happened yet. We had been preparing for this for the last three weeks, maybe six months, and it worked out well,” said an out-of-breath Van Meekeren after the win.
Both Netherlands and Ireland were hard done by rain abandoned games in their respective second outings after losing their opening matches to Bangladesh and Oman.
Later on Sunday, Bangladesh will fight it out with Oman for a place in the Super 10s.