The South Korean picked the ball up on the edge of his own box, ran away from two players and skipped past two challenges before slotting beyond Nick Pope.
Son dribbled 71.4 metres in only 11 seconds with a goal he described as "unbelievable".
"It's a big honour for me especially with this special goal," he said.
"As soon as I got the ball, I tried to find a pass and I was a bit lucky, I dribbled into the space where no-one was.
"I tried to finish it well because the action before was really quick. I was really focused on my finishing - it was an amazing feeling."
The 27-year-old wins the award for a second time, after his November 2018 accolade for a similar run and finish against Chelsea.
Son was chosen by a panel of experts combined with a public vote, beating seven other contenders.