Chasing 258 to win on a good wicket and a fast outfield, England needed to score at a run a ball for the last 20 overs. They then needed 24 off the last four overs but they picked up a priceless 13 off the 47th over.
The Somerset all-rounder Matt Bulbeck, who finished with 37 not out off 28 balls, hit the winning runs in the final over with a flick over midwicket for four off Hayden Shaw.
England's win was set up by a superb 105 from 131 balls from Gough, their captain. Earlier, New Zealand, who won the toss, had looked set for a huge total when the opener Tim McIntosh, who made 93, and Jarrod Englefield, with 73, put on 139 for the second wicket. But both batsmen were dismissed by Bulbeck in the space of four overs.
One day; New Zealand Under-19 won toss
NEW ZEALAND UNDER-19
M Papps c Wallace b Logan 31
T McKintosh c Wallace b Bulbeck 93
*J Englefield lbw b Bulbeck 73
B Patton c Fearick b Dawson 1
J McNamee c Gough b Symington 12
P McGlashon not out 24
M Gillespie c Dawson b Logan 1
M Hendry run out 0
J Franklin not out 1
Extras (b1, lb9, w7, nb4) 21
Total (for 7, 50 overs) 257
Fall: 1-60, 2-199, 3-203, 4-222, 5-243, 6-248, 7-249.
Did not bat: W McSkimming, H Shaw.
Bowling: Bulbeck 10-0-49-2; Logan 10-0-54-2; Symington 8-0-33-1; Haywood 7-0-29-0; Fearick 7-0-38-0; Dawson 8-0-44-1.
*M A Gough st McGlashon b Franklin 105
I N Flanagan run out 3
R J Logan c Franklin b Gillespie 5
I R Bell c Hendry b Shaw 24
M A Carberry b Shaw 23
R K J Dawson c McKintosh
b McSkimming 25
M P Bulbeck not out 37
M J Symington run out 1
G R Haywood st McGlashon
b Gillespie 21
J R J Fearick not out 0
Extras (lb2, w8, nb6) 16
Total (for 8, 49.2 overs) 260
Fall: 1-16, 2-26, 3-83, 4-158, 5-181, 6-208, 7-218, 8-256.
Did not bat: M A Wallace.
Bowling: Gillespie 10-1-55-2; Hendry 10-0-72-0; McSkimming 10-1-35-1; Shaw 9.2-1-33-2; Franklin 10-0-63-1.
Umpires: C Robinson and G Baxter.