Son sends Tottenham into top four, more pain for Pochettino's Chelsea
An action-packed afternoon also saw Newcastle come from 3-1 down to stun West Ham 4-3 and Fulham hit back for a 3-3 draw at bottom-of-the-table Sheffield United.
Son Heung-min's late winner fired Tottenham into the Premier League's top four with a 2-1 win over Luton as Chelsea twice blew a lead against 10-man Burnley in a 2-2 draw on Saturday.
An action-packed afternoon also saw Newcastle come from 3-1 down to stun West Ham 4-3 and Fulham hit back for a 3-3 draw at bottom-of-the-table Sheffield United.
Spurs have now come from behind to win in four of their last five home games and needed another second-half turnaround to keep their challenge for a return to the Champions League next season on track.
Tahith Chong's strike after just three minutes gave Luton a shock lead, but the Hatters ended the day in the relegation zone as their winless run extended to 10 games.
An Ange Postecoglou half-time substitution again made an impact for Tottenham as Brennan Johnson's cross was turned into his own net by Issa Kabore just six minutes after the Welsh international's introduction.
Son had missed a number of chances earlier in the game but finally got some fortune when his deflected effort trickled past Thomas Kaminski for his 15th goal of the season.
Chelsea boss Mauricio Pochettino was met with another backlash at Stamford Bridge after his side failed to make the most of an extra man for the entire second half against second-bottom Burnley.
The Blues appeared on course to cruise to victory after Lorenz Assignon was harshly sent-off for pulling down Mykhailo Mudryk inside the area.
Burnley boss Vincent Kompany was also shown a red card for taking his protests too far.
Cole Palmer coolly chipped in the resulting penalty, but the 10 men levelled two minutes into the second half thanks to Josh Cullen's super finish from outside the box.
Raheem Sterling had been booed off in Chelsea's FA Cup quarter-final win over Leicester a fortnight ago but thought he had set up the winner in style with a flick that Palmer stroked into the far corner.
Chelsea, though, failed to hold out again as Dara O'Shea headed in a corner nine minutes from time to leave Pochettino's men still in the bottom half of the table.
Newcastle closed to within one point of West Ham in seventh after a remarkable fightback at St. James' Park.
Goals from Michail Antonio, Mohammed Kudus and Jarrod Bowen wiped out the advantage given to Newcastle by Aleksander Isak's early penalty.
However, a second Isak spot-kick 13 minutes from time sparked the turnaround before substitute Harvey Barnes struck twice to send Eddie Howe scurrying down the touchline in celebration.
Newly-capped England international Anthony Gordon had been involved in three of the four Newcastle goals but was then sent-off in stoppage time for kicking the ball away.
"A lot of emotions in that game, we were swinging all over the place," said Howe.
"The last 10 minutes was amazing to be part of."
Everton's winless run stretched to 12 Premier League games after a 2-1 defeat at Bournemouth to leave the Toffees still perilously placed just three points above the relegation zone.
Nottingham Forest edged out of the bottom three on goal difference in their first match since receiving a four-point deduction as Chris Wood salvaged a 1-1 draw against Crystal Palace.
Sheffield United were denied just their fourth win of the season by Fulham's late fightback at Bramall Lane.
Ben Brereton Diaz struck twice as the Blades led 3-1 with four minutes of the 90 left only for Bobby DeCordova-Reid and Rodrigo Muniz to snatch a point for the visitors.
Aston Villa can go back above Tottenham into fourth when they host Wolves later.
Manchester United are now nine points adrift of the top five and desperately need to beat Brentford in Saturday's 2000 GMT kick-off to maintain their hopes of Champions League football next season.
All of the three title challengers are in action on Sunday.
Liverpool have the chance to go top when they host Brighton before Manchester City and Arsenal kick-off at the Etihad in a clash of huge significance in the title race.