Johnson, signed from Plymouth in January, salvaged a point for Wednesday with an 86th-minute equaliser after the visitors had twice taken the lead through Dean Bowditch and Paul Huntington. Gary Madine headed home his first goal for Wednesday following his arrival from Carlisle, while Luke Ayling and Adam Virgo were sent off within five minutes of each other just after the hour-mark.
The Yeovil opener in the 15th minute had an element of luck as the ball looped over Owls goalkeeper Nicky Weaver as Tommy Spurr attempted to block Bowditch's shot, but there was nothing lucky about the Owls' equaliser in the 36th minute as Spurr's incisive cross was headed home by Madine.
The visitors regained the lead in the 57th minute when Huntington headed home a corner.
Ayling received his second yellow card in the 64th minute and Yeovil were down to nine men four minutes later when Virgo was red carded while conceding a penalty.
The subsequent spot kick was scored by Giles Coke and then ordered to be retaken and missed Coke, but the Owls peppered the visitors goal and Johnson fired home with four minutes remaining.