Ospreys and Bridgend lock Lloyd Peers will captain the side, replacing squad captain Macauley Cook in the starting line-up. Elsewhere in the pack, WillGriff John replaces Will Taylor at tight head, while fit-again Thomas Young takes his place on the openside flank, alongside Ed Siggery and Owen Sheppeard who starts ahead of Ben Thomas at No 8.
Behind the scrum there is a new half-back pairing, with Blues and Pontypridd scrum half Lewis Jones getting the nod over Jonathan Evans, and Steve Shingler moving from full back to outside half in place of Matthew Morgan.
The centre partnership is unchanged, while there will be a Scarlets academy pair on the wings, with Dale Ford making his Wales Under 20 debut and Iolo Evans making his first start after coming on against Argentina.
Liam Williams moves from wing to full back.
Webster said: "We were pleased with the result against Argentina, it's great to be able to have that platform to build on, but there were a number of areas we need to improve on if we are to do well against New Zealand.
"We are lucky that due to the fierce competition within the camp for every position, this side is every bit as strong as the starting line-up selected against Argentina. Every player selected for tomorrow's game fully deserves his chance, while those on the bench will also be desperate to show what they can do against the world champions if they get the opportunity.
"Some areas of our game worked well against Argentina, including our defence, and some of our attacking play, but I felt that we got a bit lazy once we'd scored a few tries. It's going to be a different proposition against New Zealand and we will have to make a step up in intensity and concentration.
"Lloyd Peers is one of the true leaders within the squad, giving him the captain's armband for this game is a natural progression for him."
Wales U20 v New Zealand (Stadio Mario Battaglini, Rovigo, Tuesday 14 June, 5.10pm UK time, Live on S4C)
Wales team v New Zealand: Liam Williams (Llanelli); Iolo Evans (Scarlets / Llanelli) Owen Williams (Blues / Cardiff), Lewis Robling (Dragons / Newport), Dale Ford (Scarlets / Llanelli); Steve Shingler (London Irish), Lewis Jones (Blues / Pontypridd); Rhodri Jones (Scarlets / Llanelli), Kirby Myhill (Scarlets / Llanelli), WillGriff John (Blues/ Pontypridd), Lloyd Peers (capt, Ospreys/ Bridgend), Cory Hill (Blues / Pontypridd), Edward Siggery (Pontypridd), Thomas Young (Blues / Cardiff), Owen Sheppeard (Blues / Pontypridd).
Replacements: Jamie Sollis (Dragons / Cross Keys), WillTaylor (Ospreys / Swansea), Macauley Cook (Blues / Cardiff), Luke Hamilton (Blues / Glamorgan), Jonathan Evans (Dragons / Newport), Matthew Morgan (Ospreys / Swansea), Ross Jones (Ospreys / Bridgend)