Spurs were forced to come from behind after the hosts had taken an early lead through Junior Stanislas, but Dele Alli levelled things up before half time to send the two sides into the break all square.
Son then delivered on Mother's Day with a second-half brace to effectively take the game beyond Bournemouth, and Serge Aurier capped off the scoring in stoppage time as Tottenham made it four Premier League wins in a row and 12 league games without defeat.
It wasn't all good news for Mauricio Pochettino's side, though, as they lost star striker Harry Kane to an ankle injury in the first half, while Danny Rose and Alli were also forced off with injuries later in the game.
Tottenham were looking to bounce back from the disappointment of being knocked out of the Champions League at the hands of Juventus in midweek, but the visitors seemed to be suffering a hangover after Wednesday's defeat at Wembley as Bournemouth came flying out of the blocks.
The Cherries should have broken the deadlock even before their early opener when they cut through the Spurs defence with their first attack of the game, but they failed to make the most of a two-on-one break as Stanislas lifted his finish against the crossbar after being found by Lys Mousset.
Stanislas atoned for that miss just three minutes later, though, as he collected Adam Smith's cross in the area before arrowing a low finish across goal and into the bottom corner.
Spurs had failed to win any of the games in which they had fallen behind this season prior to this afternoon, and it almost got worse for them as Bournemouth continued to apply the early pressure, with Charlie Daniels turning a corner over the crossbar after more good work from Stanislas.
The visitors did manage to weather that early storm without suffering any further damage, though, and they had the ball in the back of the net themselves shortly before the half-hour mark, only for Kane's finish to be correctly ruled out for offside.
There was more bad news for Spurs too as Kane was caught by Asmir Begovic while converting the chance, forcing the Premier League's joint-top scorer off with an ankle injury with more than 10 minutes remaining in the first half.
Kane's absence actually coincided with an improvement from Tottenham, though, and Alli snatched at one volley before levelling things up for Pochettino's side moments later.
A quick move involving Kane's replacement Erik Lamela and Son released Aurier down the right flank, and his cross into the middle was turned home by Alli for his first goal in his last 16 appearances across all competitions.
Spurs almost added a second to take the lead into half time when Christian Eriksen found space to shoot, but Begovic eventually collected the Dane's low strike at the second attempt.
Bournemouth again made a quick start to the second half and almost regained their lead within two minutes of the restart when Davinson Sanchez's clearance only went as far as Simon Francis, whose subsequent drive was turned around the post by Hugo Lloris.
Eriksen then drew another save from Begovic before Bournemouth were back on the front foot, but Dan Gosling could only drag his finish well wide of the target when he should have done better from the edge of the box.
Spurs were seeing the vast majority of the ball, though, and the visitors took the lead shortly after the hour mark when Alli's cross to the back post picked out Son, whose scrappy volleyed finish bounced over Begovic and Nathan Ake on the line.
It was Son's sixth goal in his last four games, and he almost improved that tally even further just three minutes later with a powerful drive from a tight angle which Begovic needed to turn behind.
Francis threatened with another drive from outside the area as Bournemouth went in search of an equaliser, and having already lost Kane, Spurs were forced into another change through injury nine minutes from time when Rose limped off.
The Cherries thought that they had levelled things up moments later when Callum Wilson turned the ball past Lloris, but the whistle had already gone for a foul against Wilson on Sanchez.
Just seconds after that let-off there was another blow for Spurs as Alli became the third player to limp off through injury, but there was better news late on as Son doubled his personal tally for the afternoon to kill the game off once and for all.
The in-form South Korean was allowed to race clean through on goal from inside his own half, and he used the run of Lamela in support as a dummy before taking the ball past Begovic and sweeping his finish into the empty net.
Son was again sent through on goal just a minute later, and while this time Begovic was able to deny him his hat-trick, the Bournemouth keeper was at fault as Spurs added a fourth in stoppage time.
Begovic could only touch Kieran Trippier's cross into the path of Aurier, who was left with a simple headed finish into an empty net as Bournemouth's six-match home unbeaten run came to a shuddering halt.
The defeat is only Bournemouth's second in their last 11 league games and leaves them still six points above the relegation zone with eight games of the season remaining, while Spurs climb up to third having taken full advantage of Liverpool's loss at Manchester United on Saturday.
Pochettino's side also restore their five-point gap to fifth-placed Chelsea and remain unbeaten in the league this calendar year, providing an instant response to their Champions League disappointment ahead of next weekend's FA Cup quarter-final with Swansea City.
BOURNEMOUTH (4-4-1-1): Begovic; Francis, S Cook, Ake, Daniels (Ibe, '67'); Smith, L Cook, Gosling, Stanislas (Defoe, 76'); Mousset (King, 67'); Wilson
TOTTENHAM (4-2-3-1): Lloris; Aurier, Sanchez, Vertonghen, Rose (Trippier, 81'); Dembele, Wanyama, Eriksen, Alli (Sissoko, 86'), Son; Kane (Lamela, 34')