With the Championship visitors trailing, winger Johnson - who had been on the pitch just 18 minutes - clashed with Ben Pringle and head-butted the midfielder, earning a straight red.
All the goals came in the first half of this pulsating derby clash in front of a sell out 11,433 crowd, in which kick-off was delayed for 15 minutes due to congestion outside the New York Stadium.
The home side went in front when Kari Arnason's long throw was cleared to the unmarked Pringle and the midfielder lashed a rasping 20-yard effort past Chris Kirkland with just 10 minutes gone.
With a rare break forward Wednesday won a free-kick 30 yards out which was struck low with precision by Rhys McCabe to level after 23 minutes.
But another Arnason throw-in fell to Frecklington, who restored Rotherham's lead with a sweet strike after 38 minutes - his third goal in the opening two games of the season.
Rotherham hung on to their lead in the second half as Johnson was duly sent off after 76 minutes.
- Sports & Recreation
- Ben Pringle
- Kari Arnason