Blues started the second half a lot brighter and Darren Carter equalised on 51 minutes with a superb left foot volley from the edge of the box from an outswinging corner.
Everton regained their one goal advantage on 57 minutes through Chadwick again but Blues drew level for a second time just two minutes later when Kirovski headed home after Toffees keeper Richard Wright fumbled a Stan Lazaridis cross.
Former Aston Villa and Newcastle full back Steve Watson regained the lead again for Everton on 67 minutes only for Kirovski to equalise again for Blues with a strike from inside the box with only seven minutes left on the clock.
And, Kirovski capped-off a memorable first competetive match in a Blues shirt by completing his hat-trick with a shot from 12 yards out after good work on the left flank by Blues' man-of-the-match Craig Fagan.
Blues Reserves 4 Everton Reserves 3
Carter ( 51) Chadwick (30, 58)
Kirovski ( 59, 83, 87) Watson (67)
Blues: Bennett, Beauchamp, Hutchinson, Capaldi, Woodhouse, Eaden, Fagan (Hyde 72), Carter, Grondin, Lazaridis, Kirovski. Subs: Davies, Parker, Hyde, Luntala, Evans
Everton: Wright, Watson, Naysmith, Pilkington, Southern, Gemmill, Osman, Carsley, Ferguson, Chadwick, McLeod. Subs: Simonsen, Crowder, Brown, Carney, Moogan