Second-rower Price and wing Purdy both started the record-breaking win over USA in the final qualifying match and will be among the replacements for the semi-final.
England last played New Zealand in the 2011 Final, a game the Baby Blacks won 33-22.
Head coach Nick Walshe said: “We’re delighted to be in the top four and to have the opportunity to face New Zealand is a real honour.
“We’re under no illusions as to how hard the game will be, but we just need to concentrate on ourselves and on our performance.”
Kick-off on Tuesday is at 7.45pm GMT and live coverage of the game is on www.irb.com and on Sky Sports 2.
England Under-20s (v New Zealand)
15 Jack Nowell (Exeter Chiefs)
14 Anthony Watson (Bath Rugby)
13 Harry Sloan (Harlequins)
12 Sam Hill (Exeter Chiefs)
11 Ben Howard (Worcester Warriors)
10 Henry Slade (Exeter Chiefs)
9 Alex Day (Northampton Saints)
1 Danny Hobbs-Awoyemi (Northampton Saints)
2 Luke Cowan-Dickie (Exeter Chiefs)
3 Scott Wilson (Newcastle Falcons)
4 Elliott Stooke (Gloucester Rugby)
5 Dominic Barrow (Leeds Carnegie)
6 Ross Moriarty (Gloucester Rugby)
7 Matt Hankin (Saracens)
8 Jack Clifford (Harlequins) (c)
Replacements:
16 Scott Spurling (Saracens)
17 Alec Hepburn (London Wasps)
18 Tom Smallbone (London Irish)
19 Tom Price (Leicester Tigers)
20 David Sisi (Bath Rugby)
21 Callum Braley (Bristol Rugby)
22 Ollie Devoto (Bath Rugby)
23 Henry Purdy (Leicester Tigers)
