Andrew Strauss led the 293-run chase with 88 with assistance from Jonathan Trott (62) and Kevin Pietersen (39)
All-rounder Ryan ten Doeschate earlier struck a magnificent hundred to help the Dutch post a challenging 292-6.
England were disappointing from the off with dropped catches and poor bowling marring their Group B opener.
Alexei Kervezee and Wesley Barresi began well for the Dutch before Tim Bresnan got the breakthrough, removing Kervezee with the score at 36.
Barresi fell soon after when Graeme Swann struck in his first over on his return to the side with Matt Prior taking the stumping.
However, Tom Cooper and Ten Doeschate came together and took the total beyond 100 with their impressive partnership of 78.
Paul Collingwood forced a poor shot from Cooper, chipping to James Anderson at midwicket. The Netherlands then looked to be in trouble when Swann had Bas Zuiderent caught at slip.
But South Africa-born Ten Doeschate proved his quality and continued his impressive stroke play with Tom De Grooth as he powered towards three figures.
Stuart Broad returned after his opening spell to eventually remove De Grooth for 28 but the Dutch were already well on their way to posting a competitive score.
There was to be further resistance from Peter Borren, and Ten Doeschate shepherded him to great effect to give himself the majority of the strike and take their sideÃ¢â‚¬â„¢s total forwards. Borren had faced just 13 balls when the pairÃ¢â‚¬â„¢s partnership passed 60.
Ten Doeschate then passed his hundred in the 42nd over before his 119 became the highest total posted by an associate nation player against a Test-playing side.
He was eventually caught in the deep off of Broad after Borren had smashed his way to an unbeaten 35, taking a particular liking to an off-colour James Anderson.
The Dutch total of 292-6 was the highest by an associate nation at a World Cup.
EnglandÃ¢â‚¬â„¢s performance thus far had been marred by an appalling fielding display to leave Holland with a real chance of causing a shock upset.
But Strauss and Pietersen answered their critics in the emphatic fashion as they dominated the Dutch attack from the off.
Pietersen bullied with his footwork and power, relishing his new role at the top of the order as the pair put on a century partnership for the first wicket inside 18 overs.
Pietersen went when he chipped to cover off left arm spinner Pieter Seelaar for 39.
Trott joined Strauss and neither showed any reaction to PietersenÃ¢â‚¬â„¢s departure as they constructed a 50 partnership from 60 balls to keep England steadily on course for their total.
England appeared to be in cruise control until Strauss, on the verge of a ton, was well caught in the deep by Cooper off of Mudassar Bukhari for 88.
The skipperÃ¢â‚¬â„¢s dismissal brought Ian Bell to the crease and another partnership of 51 from 59 edged England closer.
Trott was then fantastically stumped down the leg side by Barresi for 62 off centurion Ten Doeschate.
Ten Doeschate then struck again, bowling Bell for 33 middle stump off an inside edge to set English nerves jangling.
With Ravi Bopara now at the crease, the 47th over saw Collingwood flick a crucial boundary over fine leg as the pairÃ¢â‚¬â„¢s hard running left them needing 23 from the final three overs.
A deft reverse sweep brought them three as England veteran Collingwood showed all his experience to take his side to the penultimate over requiring 13 from 12.
Bopara then struck a flat six over the long off fielder to take England to within touching distance of the target before swatting another four over midwicket.
He then repeated the shot off a full toss to seal an unconvincing win for England who next face India on Sunday.
MORE: The latest football news
MORE: The latest tennis news
BIOGRAPHY: Adam Lallana
BIOGRAPHY: Nacho Monreal