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Schofield took five wickets for 107 off 45 overs, after being hit for 21 runs from his first two overs and Kirtley weighed in with four for 80 as North Island were bowled out for 371 - a lead of 35.
Looking back at his lengthy bowling stint, Schofield said he had to bowl with discipline and hope for a lucky break.
"It's not a responsive wicket for spin and it's a good batting track, so I just had to bowl as tightly as possible and hope that I'd get a bit of luck, which happened," he said.
"For the last year or so I've been trying to learn how to bowl on non-turning wickets and I've found I have to be really patient, whereas on a turning track I'm used to taking wickets straight away.
"It's not the sort of track where you bowl the batsmen out; they get themselves out. I've always wanted to bowl the magic ball every ball, but I've found out that doesn't happen so all I've been trying to do is bowl a constant line, a good length and hope for mistakes by the batsmen."
Matthew Sinclair proved the star at the crease for North Island, reaching 182 off 371 balls, before being caught by David Sales at point off Schofield.
No sooner had North Island moved into the lead than they lost two wickets in as many overs to Schofield. Brooke Walker (0) went at short leg first ball and Chris Nevin (23) followed the same path as Sinclair.
Schofield secured his fifth wicket when Mark Jefferson (19) offered up a catch to short leg, leaving the deserving Kirtley to pick up the final two wickets of the innings before North Island could establish a lead of any substance.
The pitch was still batsman friendly when England A set out in the middle again and by stumps had wiped off the arrears to move into a lead of 71 for the loss of one wicket.
Michael Gough (44no) and Ian Ward (38) moved through to tea hitting some crisp boundaries and looking in command.
The only wicket England A lost came in the 26th over when the openers had put on 80, Ward caught by James Marshall.
However, with Vikram Solanki (21no) joining Gough, there were no further alarms before the close.
Scorecard:
England 1st innings total: 336
North Island 1st innings
MD Bell b Franks 0
BA Pocock lbw b Kirtley 2
MS Sinclair c Sales b Schofield 182
L Vincent c Solanki b Schofield 45
JAH Marshall c Ward b Kirtley 61
CJ Nevin c Sales b Schofield 23
BGK Walker c Ward b Schofield 0
MR Jefferson c Ward b Schofield 19
AJ Penn lbw b Kirtley 11
DR Tuffey c Turner b Kirtley 1
KP Walmsley not out 3
Extras (lb 6, w 1, nb 17) 24
Total (all out, 148.5 overs) 371
FoW: 1-0, 2-13, 3-115, 4-269, 5-329, 6-337, 7-338, 8-361, 9-364, 10-371.
Bowling: Franks 27 7 76 1; Kirtley 25.5 5 80 4; Alleyne 21 8 45 0; Davies 29 10 52 0; Schofield 45 13 107 5; Solanki 1 0 5 0
England 'A' 2nd innings
MA Gough not out 44
IJ Ward c Marshall b Walker 38
VS Solanki not out 21
Extras (nb 3) 3
Total (1 wicket, 43 overs) 106
To Bat: A Habib, DJG Sales, *MW Alleyne, +RJ Turner, CP Schofield, PJ Franks, RJ Kirtley, MK Davies.
FoW: 1-80.
Bowling: Penn 11 0 44 0; Walmsley 5 1 10 0; Tuffey 7 2 22 0; Walker 14 4 26 1; Jefferson 6 4 4 0 .
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