But the north Londoners rose to the challenge with a second half goal spree in the rain-soaked west midlands.
James Maddison put Tottenham ahead and Brennan Johnson doubled their lead before Villa captain John McGinn was sent off for chopping down Destiny Udogie.
Son Heung-min and Timo Werner struck in stoppage-time to leave fifth placed Tottenham just two points behind Villa with a game in hand.
Restoring Tottenham to Europe’s elite club competition in his first season in charge would be a significant achievement for Postecoglou and the target is now firmly in his control.
The Australian this week said reaching the Champions League would not be “a Willy Wonka golden ticket” for his club.
But the defeat left Villa feeling as sick as Augustus Gloop, the gluttonous boy who gets in trouble while visiting Wonka’s chocolate factory in Roald Dahl’s book.
Villa are hoping to reach the Champions League for the first time since 1983, but this was a major setback to their unexpected bid for a top four finish.
Unai Emery’s team claimed an early penalty when Ollie Watkins was sent flying by Micky van de Ven’s crunching challenge, but VAR rejected their appeals.
– Spurs run riot –
In a game played at a frantic pace, Villa were left frustrated when Matty Cash poked into the side-netting from Leon Bailey’s cross.
Lucas Digne nearly broke the deadlock just before half-time with a glancing header that looped wide from McGinn’s cross.
Tottenham lost Van de Ven to an injury immediately after the interval, but the visitors were unfazed as they snatched the lead in the 50th minute.
Pape Sarr beat the Villa offside trap and whipped in a teasing cross that Maddison adroitly volleyed past Martinez from five yards before celebrating with his dart-throwing routine in front of the Tottenham fans.
Villa were shell-shocked and there was worse to come for Emery’s men three minutes later.
Ezri Konsa took too long on the ball before playing a weak pass that was intercepted by Kulusevski.
Son pounced on the loose ball, drove towards the Villa area and slipped his pass to Johnson, who fired high into the net before emulating Maddison’s darts tribute.
Johnson’s goal meant Tottenham had equalled their club record streak of scoring in 27 successive league games since the start of a season.
As a gloomy silence settled over Villa Park, McGinn’s frustration reached boiling point in the 65th minute.
Lunging into a reckless tackle on Udogie, the Villa captain was immediately shown a red card that he could have no complaints about.
With Villa in tatters, Son finished off Kulusevski’s cross with a first-time strike in stoppage-time.
Werner’s composed finish from Son’s pass in the final moments underscored Tottenham’s superiority.
AFP