Ben White then saw his blushes spared with 15 minutes gone after he was pounced on by Son, who found Solanke in the area, but he was too easily dispossessed by William Saliba.
Moments later, Saliba then found his name in referee Jarred Gillett’s book for failing to return the ball after a foul on Solanke. It was the first of seven bookings of a fiercely contested first period.
As the half wore on Arsenal came into the game. Kai Havertz’s header from Gabriel Martinelli’s cross was well-saved by Guglielmo Vicario before the Brazilian should have put the Gunners ahead.
Leandro Trossard’s exquisite through-ball put Martinelli one-on-one with Vicario, but the winger’s effort was tame and his weak effort was comfortably gobbled up by the Spurs keeper.
Jurrien Timber’s challenge on Pedro Porro then sparked a brawl on the touchline with both the Arsenal defender and Vicario front and centre. Both men were booked but Timber escaped a red card for going over the top of the ball following a VAR check.
The hour mark arrived with Van de Ven’s header - straight down Raya’s throat from a James Maddison cross - the only real chance of the second period up to that point.
Arsenal looked threatening on the counter-attack with Bukayo Saka’s shot deflected behind off Porro, and from the ensuing corner came the breakthrough.
Gabriel ghosted off Cristian Romero, and with Vicario blocked off, the Brazilian headed home unmarked from a handful of yards out. It was Arsenal’s 23rd goal from set-pieces since the start of last season - more than any club in the league.
Spurs have been the masters of late goals in front of their own supporters during the Postecoglou era, and they wanted a penalty with eight minutes remaining when Gabriel took the ball off Solanke, but Gillett waved away their appeals.
Kulusevski came closest to finding an equaliser but his long-range effort fizzed agonisingly over the bar as Arsenal saw out five minutes of injury time to claim three successive derby wins at Tottenham for the first time since 1988.
“I thought it was a tight game all the way along. we controlled it for the most part and got off to a good start,” Postecoglou told BBC Sport afterwards.
“We didn’t capitalise on the opportunities and we were unable to get on top of them.
“We lost concentration [for the goal]. We’ve got some big guys in there who really attack the ball and we just switched off for a second.
“I think I’ve said my piece. For the most part we controlled the game today, had good territory and possession but we didn’t make the most of it and we got punished.”
English Premier League results
Saturday
Manchester Utd 3 Southampton 0
Sunday
Liverpool 0 Nottingham Forest 1
Manchester City 2 Brentford 1
Fulham 1 West Ham 1
Crystal Palace 2 Leicester City 2
Brighton 0 Ipswich Town 0
Aston Villa 3 Everton 2
Bournemouth 0 Chelsea 1
Today
Tottenham 0 Arsenal 1
Wolves 1 Newcastle 2