Bournemouth now sit in 12th position in the standings, but Spurs could be left with work to do in their final fixture against Everton in order to qualify for next season's Champions League.
Cherries boss Eddie Howe opted to hand a first-team debut to goalkeeper Mark Travers, but the 19-year-old was almost embarrassed within eight minutes as Lucas Moura sent a shot from the halfway line over the youngster's head and marginally wide of the post.
However, Travers quickly showed that he had settled into the game with a sharp save from Dele Alli, and that was followed by a Moura strike from inside the area being tipped over the crossbar.
The Brazilian was then successful in beating the offside trap before firing straight at Travers from an acute angle, while the Irishman also managed to divert a powerful Alli header over the bar.
Spurs were in full control of the contest with 10 minutes of the first half remaining, but Eric Dier should have been handed a second yellow card when preventing Josh King from launching a counter-attack by the halfway line.
However, Spurs' luck with the referee ran out when Son was handed a straight red card for pushing Jefferson Lerma to the ground, with the South Korean reacting to the midfielder attempting to kick the ball out of his hands before a free kick.
Mauricio Pochettino made the decision to make two substitutions at half time, but it backfired on the Argentine as Foyth was dismissed within three minutes of his introduction for a studs-up challenge on Jack Simpson.
Spurs were left with little choice but to try to secure an unlikely point, but their restricted approach worked with only a low effort from Ryan Fraser forcing Lloris into any kind of save before the hour mark.
Bournemouth eventually rallied with Wilson glancing a header wide of the target and Jordon Ibe seeing a long-range attempt punched cleared by Lloris, but Spurs went into the closing 15 minutes looking comfortable at the back.
Howe introduced Lys Mousset in an attempt to change the dynamic in the final third, and it almost paid off within two minutes as the attacker headed straight at Lloris from 12 yards out.
Spurs had their moments going forward as full time approached, but Pochettino watched his side finally succumb from a set piece in the first minute of added-on time.
An inswinging corner from the left found the run of Ake, who was able to move through a pack of players to send a header into the bottom corner from six yards.
Pochettino and his squad will be left dejected given their effort during the second half, but Spurs will still finish in the top four if they can get the better of Everton next weekend.
BOURNEMOUTH (4-4-1-1): Travers; Clyne, S.Cook, Simpson, A.Smith; Ibe (Mousset 76'), Lerma, Ake, Fraser; King; Wilson
TOTTENHAM HOTSPUR (4-2-3-1): Lloris; Trippier, Sanchez, Alderweireld (Foyth 46'), Rose; Dier (Wanyama 46'), Sissoko (Davies 82'); Alli, Eriksen, Son; Moura