Spurs are yet to find consistent form as they aim to return to the Champions League following a fifth-place finish last season, winning back-to-back league matches just once in their opening 10 league games this season.
But while they have been unable to match their superb start under Postecoglou last term - they began November 2023 top of the table - they continue to show remarkable resilience under the Australian.
Having responded to the disappointing defeat at Palace by beating Manchester City to reach the EFL Cup quarter-finals in midweek and continue their pursuit of a first piece of silverware since 2008, here they conceded the opening goal for the 12th time in 14 home league games in 2024.
However, by full-time they had equalled the Premier League record for home wins when conceding first in a single year - with this the eighth occasion.
Villa's opener came against the run of play but via a familiar vulnerability for the hosts, with a combination of Pedro Porro and Rodrigo Bentancur diverting Digne's set-piece towards Guglielmo Vicario, who could only parry the ball into Rogers' path.
The hosts were relieved to see Ollie Watkins, kept quiet for much of the first half, fail to double the advantage when he dragged his shot wide before half-time.
But the equaliser early in the second half ignited Spurs, who emerged from the break with renewed intent while preventing Villa landing any attempts on target.
Captain Son played a key role on his return from a two-game injury-enforced absence, but the South Korea forward was visibly surprised to be substituted only a few minutes after assisting Johnson's leveller.
That allowed Solanke to take centre stage, the 27-year-old showing his class particularly with his first, and Postecoglou will hope his big-money addition can continue to build confidence to aid his team's search for consistency.
"There is great belief in these players. We stick to our principles and when we do that we are hard to stop," said Postecoglou.
"I felt the momentum was going our way, we knew we would finish strong and if we upped it a couple of gears, like we can, we knew we would be hard to stop."