Tensions simmered from the moment Neal Maupay fired Brentford into a first-half lead and celebrated by copying James Maddison’s darts celebration in front of the home end to wind up his hosts.
Some players were still bickering at the final whistle although Maddison and Maupay made their peace and Spurs had survived the scare.
That did not look likely at the interval but Postecoglou made two key changes, reshuffled his team and they exploded into life with three goals in 10 minutes at the start of the second half.
Destiny Udgoie equalised and Brennan Johnson made it 2-1 within seconds before Richarlison added the third.
Brennan Johnson enjoyed throwing the dart celebration back in Neal Maupay's face
Tottenham fought back in the space of ten second-half minutes to reverse the game
Maupay had trolled James Maddison's trademark dart celebration after the opener
Ivan Toney pulled one back to spark a nervous finish but Tottenham climbed above Aston Villa into fourth.
Out of all cup competitions, they have only the Premier League campaign to focus on.
Tottenham had problems in the early stages handling Brentford’s energy and aggression. The visitors winning the ball regularly in the opening exchanges and breaking into the inviting spaces behind the high defensive line always deployed by Postecoglou.
Spurs 433: Vicario 7; Porro 7, Romero 6.5, Van de Ven 6.5, Udogie 7; Skipp 6 (Hojbjerg 46, 7), Bentancur 6 (Johnson 46, 7), Maddison 6.5; Kulusevski 7, Richarlison 7, Werner 7.5 (Donley 90+1).
Subs: Forster, Gil, Royal, Davies, Scarlett
Goals: Udogie 48, Johnson 49, Richarlison 56
Bookings: Kulusevski, Donley
Manager: Ange Postecoglou 7.5
Brentford 352: Flekken 6.5; Collins 6 (Ajer 78), Pinncock 6.5, Mee 6; Roerslev 6.5 (Dasilva 78), Jensen 7 (Yarmoliuk 57, 6), Nogaard 7, Janelt 6.5 (Baptiste 88), Lewis-Potter 6.5 (Damsgaard 88); Toney 7, Maupay 7.
Subs: Strakosha, Jorgensen, Brierley, Fredrick
Goals: Maupay 15, Toney 67
Bookings: Norgaard, Maupay, Yarmoliuk,
Manager: Thomas Frank 7
Ref: David Coote 6.5
Even before Maupay’s opener, there were warnings. First, Keane Lewis-Potter broke down the left but Spurs quelled the danger. Then Mads Roerslev galloped forward on the right and found the net with a precision angled drive only to see a flag raised and the goal ruled out for offside against Mathias Jensen, who made the final pass.
Three minutes later and Brentford were ahead, a goal started and finished by Maupay, who pounced to intercept a pass by Destiny Udogie on halfway. Christian Norgaard released Ivan Toney and he looked certain to score but could not beat Guglielmo Vicario.
The Spurs goalkeeper held his nerve and stood firm, making a fine save. Maupay had continued his run in support of his strike partner, however, and bundled the rebound into the net from six yards, with a deflection off Cristian Romero on the way.
Maupay and Toney performed a cheeky darts celebration in front of Tottenham’s South Stand, which provoked a fair amount of agitation because James Maddison, making his first start since November, likes to throw pretend darts when he scores.
Maupay could not resist adding a word in Maddison’s ear as he trotted back for the restart and the pair became locked in an argument. All of which brought an element of needle to the contest and this, while wholly preposterous, worked in Brentford’s favour.
Tottenham struggled for any rhythm. They dominated possession and created a couple of first-half chances. Timo Werner forced a strong save from Mark Flekken then headed feebly wide at the back post from a corner.
Richarlison unleashed a brilliant curling effort which flashed wide and had a goal ruled out for a foul on Nathan Collins but the Bees held firm, channelling Spurs into congested areas before crowding them out, winning the ball and bursting with menace on the counterattack.
Dejan Kulusevski celebrated Johnson's goal as Tottenham roared back into it
Richarlison made it 3-1 to the home side to continue his recent upturn in form
Thomas Frank’s team were also dangerous from set-pieces and might have extended the lead before the interval. Ethan Pinnock went close with an audacious back heel after controlling a left-wing cross by Jensen with his back to goal.
Vicario saved again from Toney, who probably should have scored with a header from a free-kick. Again, the outstanding delivery came from Jensen.
Postecoglou enjoyed instant reward for two changes at half time with three goals in the opening 10 minutes of the second half.
Udogie levelled, linking up with Werner on the left. Pinnock blocked his first effort but Udogie forced the rebound past Flekken at the near post. Seconds later, Johnson fired Tottenham ahead after another explosive burst of pace by Werner, who tore down the left and served up an open goal for the substitute, who could not miss.
Johnson had the darts out to celebrate as he goaded the visitors. So did Richarlison when he made it 3-1. Udogie disturbed the Bees with a powerful run and Maddison had a shot blocked before Richarlison found the net through the legs of Collins. It was a seventh goal in seven Premier League games for the Brazilian.
Brentford seemed overwhelmed. They wobbled momentarily as if they were about to cave in and then summoned an impressive response.
The Brazilian was another to make a point of performing the dart celebration
Destiny Udogie scored just after the break to bring Spurs back on level terms
Udogie's strike came at a perfect time, with Brentford having stood firm up to the break
Richarlison scored a lovely dink over the goalkeeper but it was disallowed
Toney went close with a fierce drive from distance and then missed an excellent chance. There was only the goalkeeper to beat when he received the ball but he twisted left and right, throwing dummies in search of a better angle and eventually dragged a shot wide.
But he made no mistake when Udogie suffered an inexplicable lapse in concentration. Toney was trudging back from an offside position when Udogie gave him the ball. This time, with all the time in the world he beat Vicario.
The goal added jeopardy but the closing stages were untidy, littered with stoppages and Toney was unable to finish on a double.
Shandon Baptiste came closest to an equaliser, a volley that drew a save from Vicario and Spurs took the points.
Brentford can take plenty of positives from the performance and the way they made life uncomfortable for their hosts but they have slipped perilously close to danger, only four points clear of the drop zone and with Manchester City next.
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