Both Moriarty and Stooke were simply superb against New Zealand, as indeed were all the men in white.
England took the game to New Zealand from the very first whistle and quickly opened their account with a Henry Slade penalty. However, their opponents showed their class by responding with a try from Faiva.
A second penalty from Slade nudged England back in front, and this was quickly followed by a magnificent try from Matt Hankin after a break from Jack Clifford and an interception try from Anthony Watson.
New Zealand were rocked and could only respond with a Simon Hickey penalty to go into half time trailing 8-20.
However, they were a different animal in the second half, and it was all hands to the pumps in defence for England.
The tackling was magnificent but New Zealand seemed to have the momentum going into the final few minutes trailing just 21-23.
England could have cracked but the forwards powered over from close range, Slade adding the conversion and then a last gasp penalty to clinch an historic 33-21 win.
Head Coach Nick Walshe said:
"The lads were absolutely unbelievable. From the first minute they put their bodies on the line - they were excellent.
"We knew that New Zealand would want to play with the ball in hand, and they did. They made it very tough for us, but our defence were brilliant.
"We felt that we could have had another score before the break, but it wasn't to be and they came back at us. But we showed real character to stay in front and I'm over the moon with the win.
"Wales will be a tough challenge - we obviously know them pretty well from the Six Nations and they put in a massive performance against the South Africans, so massive credit to them and we look forward to seeing them on Sunday."