More than 50,000 fans, who had helped create a fantastic atmosphere at the National Arena, went delirious when Gabriel Torje hit the crossbar from a curling free kick.
The Dutch, who inflicted a first defeat on Romania, went ahead after eight minutes when home keeper Ciprian Tatarusanu punched the ball after an inswinging corner, only for Jeremain Lens to send a looping header beyond the defenders from outside the penalty area.
Romania have enjoyed a flying start to their campaign after beating Estonia, Andorra, Turkey without conceding a goal and their coach Victor Piturca decided to field an unchanged starting lineup.
Gheorghe Grozav, who scored the winning goal against Turkey and recovered from a groin injury just before the match, missed a chance to level the score with a fine volley.
However, the Balkan side, who have not qualified for the World Cup finals since 1998, found the fast and aggressive play of the Dutch difficult to cope with.
Unmarked Bruno Martens made it 2-0 from close range after Rafael van der Vart delivered a precise free kick but when the visitors slightly reduced the tempo Romania hit back with a superb solo effort by sole striker Ciprian Marica.
The Dutch, who stretched their run to 12 World Cup qualifying wins in a row, restored their two-goal advantage in the dying seconds of the first half when Van der Vart converted a harshly-awarded penalty.
After a lively start to the second half, chances began to dry up with Louis van Gaal's Dutch side switching to a more defensive style.
A strong Romania appeal for a penalty was waved away with less than 10 minutes remaining when Martens brought down substitute Adrian Popa in the area.
Robin van Persie, returning in the central striking role, completed the rout with an easy finish five minutes from time.
HUNGARY 3-1 TURKEY
Hungary stayed on the coat tails of Netherlands at the top of the World Cup Group D qualifying table after recovering from losing an early goal to sink Turkey 3-1 on Tuesday.
Turkey grabbed a deserved lead at the Ferenc Puskas Stadium when Caner Erkin marched down the left wing and his cross was tapped in by Mevlut Erdinc in the 22nd minute.
Hungary hit back nine minutes later as an effort from Vladimir Koman, which seemed to be intended as a cross, went in off goalkeeper Volkan Demirel.
The home team went 2-1 up in the 50th minute when Adam Szalai rounded off a sweeping counter attack.
Zoltan Gera made sure of victory with a penalty seven minutes later after Hamit Altintop felled Koman.
Hungary are level with Romania on nine points from four games, three points behind group leaders Netherlands. Turkey have three points.
ANDORRA 0-1 ESTONIA
Estonia beat Andorra 1-0 in Andorra La Vella to register their first points of the campaign.
Andres Oper's 56th-minute strike was the difference between the sides.
The result leaves the hosts bottom of the group having conceded 13 goals and not scored one.