Kick-off was delayed by 15 minutes to allow the crowd of 11,433 to find their seats at the New York Stadium on Tuesday night.
Ben Pringle smashed the Millers in front on 10 minutes after Kari Arnason's long throw found him at the far post.
On 23 minutes, Rhys McCabe drew the Owls level with a low free-kick from 30 yards.
But on 38 minutes, another Arnason long throw caused chaos in the Wednesday penalty area and O'Connor was able to knock the ball down for Frecklington to drive home from 20 yards.
In the second half, the visitors were reduced to 10 men when Jermaine Johnson was sent off for violent conduct. Johnson appeared to headbutt Pringle in an off-the-ball incident and was shown a straight red card.