Giles, the Warwickshire left-armer, grabbed 4 for 79 in 27 gruelling overs as NSW reached 215 for 5 to claim a 60-run advantage after wrapping up England's innings within three balls of their overnight 155.
The 23-year-old Giles reduced the inexperienced NSW line-up to 47 for 4 until Scott Thompson and Craig Glassock added 113 in 146 balls during the final session, which was extended to compensate for the delayed start following yesterday's torrential rain storm.
Thompson finished unbeaten on 78, including nine fours and three sixes, while Glassock was on 56 when play finished to end Giles' marathon bowling stint.
"I was pleased with the way I bowled early on but I got very tired in the final session. The heat was incredible," he said. "The last session was very long, but considering it was the first team we've bowled for about six weeks, I thought we stuck to our task well."
Second day of four; England A won toss
ENGLAND A - First Innings
(Overnight: 155 for 9; O A Shah 76)
D W Headley b Freedman 0
P M Such not out 0
Extras (lb2) 2
Total (69.5 overs) 155
Fall: 1-21 2-21 3-25 4-60 5-120 6-127 7-143 8-155 9-155.
Bowling: Alley 10-3-21-2; Clark 7-0-28-0; MacGill 25-13-43-4; Thompson 7-2-20-1; Freedman 20.5-6-41-3.
NEW SOUTH WALES 2nd XI - First Innings
J L Armberger c Headley b Giles 17
A D McQuire run out 17
*M T Haywood c Hegg b Giles 5
P Maraziotis b Giles 0
G C Rummans c Butcher b Giles 24
C A Glassock not out 56
S M Thompson not out 78
Extras (b1 lb3 nb14) 18
Total (for 5, 73 overs) 215
Fall: 1-26 2-40 3-40 4-44 5-102.
To bat: P J S Alley, D A Freedman, S Clark, S C G MacGill.
Bowling: Headley 10-2-30-0; Chapple 6-2-10-0; Giles 27-8-79-4; Such 23- 4-73-0; White 5-1-11-0; Hollioake 2-0-8-0.
Umpires: S Tausel and I Emerson.