A sellout crowd of over 45,000 in Bangkok's Rajamangala stadium were hoping for an upset after Thailand held South Korea to a shock 1-1 draw in Seoul last week.
But Son's men kept their cool in hot, sticky conditions as Park Jin-seob and Lee Jae-sun joined the Tottenham Hotspur star on the scoresheet.
After a scrappy first half, brightened only by Lee's goal, Son fired home the second from a tight angle nine minutes after the break, with the ball rattling into the net through Thai keeper Patiwat Khammai's legs.
Park sealed the win eight minutes from time as South Korea put last week's disappointment behind them.
The result means South Korea, who are top of Group C, need just a draw against Singapore in June to progress on the road to a 12th World Cup finals appearance.
Coach Hwang Sun-hong, who took temporary charge following the dismissal of Jurgen Klinsmann last month, voiced his relief at his first win in charge.
"It was a difficult match. The result was what we needed," he said.
Paris Saint-Germain's Lee Kang-in started in a front three with Son after coming off the bench last week following revelations about a bust-up between the pair at the Asian Cup.
