O'Connor scored his first inside the opening minute, finding the net from close range following Clinton Morrison's pull-back.
The experienced midfielder then made it 2-0 in the 14th minute with a fine first-time shot after meeting a low cross from Jon Otsemobor.
Ben Davies pulled a goal back for County midway through the half, curling a free-kick round the defensive wall and just inside Nicky Weaver's left-hand post.
The home side had chances to kill off the game before the break with Marcus Tudgay having a header saved and then going close with a shot. Daniel Jones also just missed the target with a free-kick.
County's Mike Edwards threatened just before the interval, heading a fraction over. Tudgay went closest to scoring in the second half, seeing his header come back off the crossbar. O'Connor had a chance to complete his hat-trick in stoppage time but he fired narrowly wide.