The South Korean superstar put the Championship side to the sword with two fabulous goals in the second half.
Debutant Arnaut Danjuma put the icing on the cake late on as the Premier League side cruised to success on the road.
It was yet another largely frustrating first half for Spurs as Preston kept them quiet in the final third, but their individual class shone through as two moments of brilliance essentially settled the tie.
Antonio Conte will hope that back-to-back victories can be used as a springboard for success on more than one front for Spurs, as their prospects in the Premier League and Champions League are still alive too.
Ryan Lowe's attentions will now turn solely on getting Preston into the playoffs, as they hope to earn promotion back to the top flight for the first time in over 60 years.
The main headline pre-game was that Spurs' main man Harry Kane was left on the bench with Son used as the central striker in attack.
That decision was likely taken with Conte looking ahead to their encounter with Manchester City in the league next weekend, and with their two-legged tie against AC Milan in Europe on the horizon too.
Son was the bright spark in the first half and was the one individual who looked most likely to make something happen.
It was an underwhelming opening 45 minutes with very little goalmouth action but Son blew the game into life early in the second half by breaking the deadlock with a super strike from 25 yards out.
After receiving a pass from Japhet Tanganga, the Tottenham number seven opened his body up and unleashed a powerful curling strike which bent around the lunging Ryan Ledson and out of reach of goalkeeper Freddie Woodman.
Having fallen behind, Preston immediately showed signs of promise in attack, pressing Spurs high and getting the ball into the area, but there was no end product to worry Fraser Forster in goal.
Ben Whiteman came closest to scoring for the hosts, but he was unable to get enough curl and conviction on his strike to keep it on target from the edge of the area.
Soon after, the tie was all but over when a nice flick from Ivan Perisic, used in a more advanced role this evening in a three-pronged attack, played Son through and he gave Woodman no chance again with another excellent hit.
Fatigue was evident among the Preston players in the final 20 minutes and Spurs added some gloss to their win when Danjuma came on and scored his first goal in Tottenham colours with just three minutes to play.
Preston had flashes but Everton loanee Tom Cannon and strike partner Ched Evans were isolated up top, and set pieces proved fruitless for much of the evening as the gulf in class was there for all to see.
This result means Spurs have now won an impressive 43 of their last 46 ties against lower-league opposition in the FA Cup.
Spurs have bigger assignments to come, starting next week when they welcome Man City to North London as they look to maintain their battle for the top four.
Bristol City are the side next on the agenda for Preston at Deepdale next Saturday.