The two Pontypridd players will join clubmates Neil Jenkins, Mefin Davies and Michael Owen in a new look Welsh side showing 10 changes in personnel from the last international against South Africa in Cape Town on June 15.
The game will also see the Pontypridd skipper Mefin Davies, lock Robert Sidoli and the Llanelli prop Martyn Madden make their first full starts in the Welsh jersey.
All three players made their debuts on last summer's South African tour - Davies was a 78th minute replacement in the second Test, Sidoli played 18 minutes in the first Test and nine minutes in the second and Madden played for three minutes in the first Test.
Parker will become the sixth New Zealand-born player to play for Wales, following in the footsteps of Hemi Taylor (24 caps - 1994-96), Dale McIntosh (2 caps - 1996-97), Shane Howarth (19 caps - 1998-2000), Brett Sinkinson (20 caps - 1999-2002) and Matt Cardey (1 cap - 2000). Parker qualifies to play for Wales having completed a three-year residency period in August.
Neil Jenkins makes his first start for Wales since lining-up against Italy in Rome 18 months ago in the 2001 Six Nations Championship.
It will be the world record points scorer's 87th appearance for his country and he will be seeking to add to the record 1,029 points he has scored for Wales.
Jenkins, Wales most capped player, will play at outside half and partner Llanelli's Dwayne Peel at half-back. Peel, who will win his 10th cap in Wrexham, played for one minute with Jenkins in the first Test against South Africa in Bloemfontein on June 8.
Jenkins has now played with nine scrum halves during his Welsh international career - Robert Jones, Chris Bridges, Rupert Moon, Paul John, Robert Howley, Andy Moore, Gareth Cooper, Ryan Powell and Dwayne Peel.
Rhys Williams reverts to full-back (centre) for the first time since Wales beat Italy 33-23 in Rome in April, 2001, while Mark Jones comes in at full back (right) to win his fourth cap having last played in the first of the two-Tests in Japan in the summer of 2001.
Bridgend skipper Gareth Thomas will join Williams and Jones to complete the back three line-up on the left hand side, gaining his 58th cap. Thomas, who last played at centre against England in March, is seven tries behind Ieuan Evans in the Welsh all-time try list with 26.
Charvis will skipper Wales for the fourth successive game and will win his 47th cap. Michael Owen will make his third start at blindside flanker and Scott Quinnell will win his 51st cap at No 8.
The game will be Wales' 514th international (271 wins, 217 losses, 25 draws) and the second played at Wrexham. It will be National Coach Steve Hansen's seventh match in charge of the Welsh side (1 win, five defeats).
WALES: Rhys Williams (Cardiff); Mark Jones (Llanelli), Tom Shanklin (Saracens), Sonny Parker (Pontypridd), Gareth Thomas (Bridgend); Neil Jenkins (Pontypridd), Dwayne Peel (Llanelli); Gethin Jenkins (Pontypridd), Mefin Davies (Pontypridd), Martyn Madden (Llanelli), Robert Sidoli (Pontypridd), Steve Williams (Northampton Saints), Michael Owen (Pontypridd), Colin Charvis (Swansea, captain), Scott Quinnell (Llanelli).
Replacements: Robin McBryde (Llanelli) or Andrew Lewis (Cardiff), Ben Evans (Swansea), Gareth Llewellyn (Neath), Gavin Thomas (Bath), Ryan Powell (Cardiff), Stephen Jones (Llanelli), Craig Morgan (Cardiff).