The League Two side showed their quality during the first half of the game as Paul Hayes scored a double for Gareth Ainsworth's side including a penalty which gave the visitors a 2-0 lead at half-time.
Spurs though in the second half were a much different team and they got themselves back on level terms in a four minute spell with goals from Son and Vincent Janssen.
Wycombe though managed to put that bad spell behind them and got themselves back in front when Gary Thompson headed home six minutes from time.
Maurico Pochettino's side weren't going to go away though as Dele Alli scored the equaliser in the 89th minute and then with the last attack of the game, Son won the game for the hosts to send the Lillywhites through to round five.
Visitor's hit the bar within a minute of the game starting
Straight from the start of the game, it was clear that the visitors weren't fazed by facing Spurs as they should have went in front barely a minute into the game.
A cross into the box was headed back across goal by Adebayo Akinfenwa into the path of the onrunning Hayes, who with the goal at his mercy, somehow saw his header hit the bar and go over.
Brillance from Hayes gave the visitor's the lead
The hosts were barely in the game in the opening half an hour and they finally fell behind midway through the first half.
A corner was whipped into the box by the visitors which the hosts failed to clear and the ball fell to Hayes, who hit a lovely left footed volley into the top corner of the net to give the League Two side a well deserved lead.
The opening goal finally woke the Lillywhites up and they almost got back on level terms when Moussa Sissoko hit a strike towards goal but Hayes, who was having an impact at both ends of the field, cleared the ball off the line.
Not long after that, Son forced Jamal Blackman into making a brilliant save which was his first meaningful action of the first half.
Hayes doubled the visitor's lead from the spot
Just when Spurs were having their best period of play in the game, they went two goals behind when Cameron Carter-Vickers brought down Sam Wood in the box and referee Roger East pointed straight to the spot.
Hayes stepped up to take the penalty and confidently sent Michel Vorm the wrong way to give the visitors a bigger lead at half-time with something really big to hang onto in the second half.
The second half though was much different for the visitors as the hosts came quickly out of the blocks and started to put real pressure on the visitor's defence.
Two goals in a four-minute spell got the hosts back on level terms
The persistence from the hosts finally paid off when they managed to get a goal back on the hour mark when Son's left footed strike from a tight angle took a deflection and went into the back of the net.
It was now all about how the visitors were going to react and they didn't as four minutes later, Spurs got themselves back on level terms.
Janssen, on as a second half substitute, was fouled in the box by Aaron Pierre and the referee pointed to the penalty spot.
Janssen stepped up to take it himself and just about managed to squeeze the ball into the back of the net past Blackman.
The hosts tails were now up and but for some last ditch tackling from the visitors then the whole tie would have been turned around very quickly.
Spurs had a problem late on though when Kieran Trippier had to go off the field with an injury and had to play the last minutes of the game with ten men as they had already made their three substitutions.
Thompson headed the visitor's back in front
The visitors managed to take advantage of that when Thompson, on as a second half substitute, headed home a brilliant Myles Weston cross six minutes from time to send the visitors on the brink of victory again.
Alli and then Son scored in stoppage time to break Wycombe's heart and send Lillywhites through the next round
Victory though wasn't meant to be as Alli managed to get Spurs back on level terms once again when Blackman's clearance was headed back into the midfielder's path and he struck the ball into the net.
The last thing that the visitor's wanted then was to see six minutes of added time at the end of the game as they really desreved at least a replay.
Janssen had a big chance to win for the hosts in injury time when he had a header from close range well saved by Blackman after a great cross from Sissoko.
Janssen's blushes were spurred though as with the last kick of the game, Son won it for the home side after a nice one-two with Moussa Dembele to break Wycombe's hearts and send the Lillywhites through to round five.