But he has now struck nine times in Tottenham’s last eight league games after putting the visitors ahead in the fourth minute and restoring their lead with a superb strike from the edge of the area in the 41st minute.
However, Everton rallied after a poor start and their tactic to target Tottenham keeper Guglielmo Vicario from corners paid off with a 30th-minute equaliser.
Jack Harrison was backing into Vicario before turning in Dominic Calvert-Lewin’s header towards goal.
And in the fourth minute of stoppage time, Tottenham’s Cristian Romero could only head James Garner’s free-kick towards his own goal and Branthwaite bundled the ball home.
“It’s obviously never going to be an easy game here. You have to deal with a fair bit but most of the time we handled it ok. Unfortunately we couldn’t hold out,” Tottenham boss Ange Postecoglou said.
Third bottom Everton have failed to win in six league games, but Toffees manager Sean Dyche said: “We deserved at least an equaliser, if not all three (points).”
Villa climbed above Tottenham thanks to their emphatic victory over the bottom of the table Blades at Bramall Lane.
Unai Emery’s side went ahead after 12 minutes when John McGinn tapped into the empty net after Ollie Watkins’ shot hit the post.
Watkins bagged the second four minutes later, slotting home from Douglas Luiz’s pass, and Leon Bailey made it three with a curler into the top corner in the 20th minute.
When Youri Tielemans drilled his shot in via the bar in the 30th minute, Villa were the first away team to score four goals in the opening 30 minutes of a Premier League game since Chelsea at Bolton in 2011.
Emery’s men showed no mercy as Alex Moreno volleyed number five two minutes after half-time.
Villa are five points behind leaders Liverpool, who visit third placed Arsenal on Sunday.
Newcastle thriller
At St James’ Park, Newcastle staged a stirring fightback to rescue a 4-4 draw against Luton.
Sean Longstaff put Newcastle ahead in the seventh minute with a clinical close-range finish from Kieran Trippier’s cross.
Gabriel Osho headed Luton level in the 21st minute when he rose to finish off Ross Barkley’s cross.
Longstaff restored Newcastle’s advantage two minutes later, but Barkley equalised five minutes before half-time.
Luton won a 59th-minute penalty after Chiedozie Ogbene was tugged by Dan Burn, the decision given after a lengthy VAR check to determine the foul was inside the area.
Carlton Morris scored but had to retake the kick due to encroachment, holding his nerve to net with his second attempt.
Elijah Adebayo’s composed strike three minutes later increased Luton’s lead, but Trippier’s 67th-minute close-range finish gave Newcastle hope.
Harvey Barnes, playing for the first time since September after injury, completed Newcastle’s escape act six minutes later with a fierce finish into the bottom corner.
“A real credit to the players for coming back because it is not easy to do. We scored some great goals and could have won it,” Newcastle boss Eddie Howe said.
Luton moved one point clear of the relegation zone, while Newcastle are in ninth place.
Brighton crushed Crystal Palace 4-1 at the Amex Stadium to bolster their bid for a European place.
The seventh placed Seagulls scored through Lewis Dunk, Jack Hinshelwood, Facundo Buonanotte and Joao Pedro as Palace fans called for Roy Hodgson to be sacked.
David Datro Fofana’s double inspired second bottom Burnley’s fightback from two goals down to draw 2-2 with Fulham at Turf Moor.
© Agence France-Presse
Photo: X/.@bartonsupremacy