Swindon got off to a poor start going behind after only 4 minutes when Lucas failed to hold onto the ball to allow Johnson to score.
Things then went from bad to worse for Swindon who were 2-0 on 8 minutes when Wright-Phillps scored from 6 yards out.
David Prutton pulled a goal back for Swindon on 37 minutes with a powerful shot, which the Plymouth keeper was unable to stop making it 1-2.
Swindon then went on to miss a few more chances before on 68 minutes being awarded a free kick just outside the area which Michael Rose took, and scored to equalise.
There were then 2 red cars as first David Prutton was sent off for his second yellow card of the game, then Plymouth were also reduced to ten men in the final minute of the game when Johnson was sent off.
With 5 minutes of stoppage time coming to an end the game was heading towards a 2-2 draw when Plymouth scored a very late winner when Wright-Phillps headed in from close range to make it 2-3.