Striker Lee Johnson, Gary's son, tried to play the ball back to goalkeeper Luke McCormick following an injury break.
But McCormick was off his line, meaning the ball soared into the net from 50 yards out.
Williamson was incensed, but Johnson senior had no hesitation in ordering his defence to step aside for Pilgrims forward Stevve Crawford to walk the abll in to an empty net for an immediate equaliser.
Johnson said: "I certainly didn¹t want to go through the hassle of FA tribunals and going through what Arsenal and Sheffield United had to, so I thought 'let them have a goal back and we¹re back where we started'
"Even after we scored, none of our players celebrated and I turned to Bobby Williamson straight away and said 'don't worry Bob, you'll be getting the next goal.
"He's a big guy and calming him down was my first job. Then I got word to my players to let Plymouth go straight down the other end and stick the ball in the back of the net.
"Crawford getting on the scoresheet at least gives Berti Vogts something to smile about at last!
"Bobby rang me the next day to express his thanks and looking back, I'm delighted with the decision we made.
"It was a true victory for sportsmanship - it's just a pity it detracted from an outstanding result for us."