With Bantams boss Stuart McCall watching on from the sidelines, the three players were included in City's starting line up along with fellow pros Daniel Devine, Vincent Rabiega and Rouven Sattelmaier.
On his first game back since a calf problem at the beginning of the season, Clarke managed to get 87 minutes under his belt while the rest of McCall's senior squad members played the full game.
City won the game 2-1 thanks to two late goals from first year apprentice striker Casey Taglione.
The Bantams were trailing with just nine minutes of normal time following Tyler Harvey's first half opener for Wrexham, but Taglione struck City level with neat finish after good work from fellow scholar Tom Windle.
Buoyed by his initial contribution after coming off the bench earlier in the half, Taglione went one better by netting the winner in final minute of normal time after Rabiega had laid the ball into his path from a Kilgallon free-kick.
Kilgallon spent most of the game at left back, with McArdle and Clarke partnered together in central defence until the latter's late substitution.
Clarke was at the heart of the game's opening chance of note when he headed wide from an early corner.
With a noticeable wind against City in the first period, Wrexham began to enjoy the better of proceedings as the half progressed.
Harvey headed narrowly wide of the near post following Callum Powell's cross before the striker went one better to give the hosts the lead in the twentieth minute.
As City tried to clear their lines from the second phrase of a set-piece, Anthony Barry's drive from distance fell at the feet of Harvey by the edge of the box and striker struck past a rooted Sattelmaier with the Bantams defence looking for offside.
City's clearest scoring opportunity in the first half came via the boot of apprentice attacker Reece Powell when his low right-footed drive from just inside the area was tipped onto the post by Wrexham 'keeper Kieran Wolland.
City shot-stopper Sattelmaier was also called upon before the half was out, with Paulo Mendes warming the hands of the German with a rising drive that was pushed over by the custodian's near post.
Helped with the wind now being at their backs, City began the second period with real purpose as they looked for a way back into the match.
Rabiega fired narrowly wide with a drive from just outside the box while McArdle sent a looping header not too far over from a corner shortly afterwards.
Rabiega threatened again minutes later, this time forcing Wolland to push the ball past his far post after a low drive from the edge of the area by the striker.
Ville Moilanen looked to get in on the action himself on the hour mark but he volleyed over from close range following Niah Payne's inviting cross.
Despite City's greater presence in the game after the break, veteran forward Gary Taylor-Fletcher could have doubled Wrexham's lead when he was found in space in the box via Doug Tharme's cross but his downward header bounced up onto the crossbar.
Taylor-Fletcher had another promising opportunity later in the half but he curled a drive from the edge of the area narrowly past the post.
Wrexham's failure grab a second goal in the game would ultimately prove costly when Taglione drew City level in the 81st minute.
After producing a strong challenge to regain possession for City, Windle picked out Taglione over by the far side of the penalty area with a great cross-field pass.
Taglione turned towards goal after receiving possession before finishing neatly with a brilliant drive low into the far bottom corner.
The stocky striker then completed the comeback for the Bantams in the ninetieth minute when he rifled low into the bottom corner from the edge of the area after Rabiega had brought down a Kilgallon free-kick into the box from deep.
CITY XI
1. Rouven Sattelmaier
2. Tom Windle
3. Matthew Kilgallon
4. Daniel Devine (c)
2. Tom Windle
3. Matthew Kilgallon
4. Daniel Devine (c)
5. Rory McArdle
6. Nathan Clarke
7. Ville Moilanen
8. Kwame Boateng
9. Vincent Rabiega
10. Niah Payne
11. Reece Powell
Substitutes:
12. George Sykes-Kenworthy (GK)
14. Sam Wright
15. Casey Taglione
16. Harry Warren
17. Omed Gardezi
Goals:
Taglione (81, 90)
Substitutions:
Taglione for Moilanen (61), Wright for N Clarke (87)