The Lilywhites emphatically got back to winning ways in the top flight against Unai Emery's side, responding to Morgan Rogers's opener through Dominic Solanke (two), Brennan Johnson and James Maddison.
However, Spurs' win came at a rather big cost, as Romero had to be withdrawn after hurting his foot while making a tackle, being replaced by Ben Davies just past the hour mark.
A few minutes before Romero was forced off the field, Richarlison came off the bench to take Son Heung-min's spot in the final third, and the Brazilian made an immediate impact with the assist for Solanke's second goal.
Richarlison was in visible pain during the celebrations, though, having seemingly tweaked a muscle during his lung-busting run into the box, and he was immediately substituted himself.
Postecoglou unsure of Romero, Richarlison injury severities
Asked for an update on both players in his post-game press conference, Postecoglou admitted that he was still in the dark about how serious their issues were, but he conceded that Romero's issue must be at least moderate if the "tough cookie" defender was forced off.
"Yeah, I know Richy obviously felt something in the action of setting the goal up, his hamstring, so we'll see," football.london quotes Postecoglou as saying.
"Romero yeah, it was in that challenge again. He felt his foot was sore. I don't have any sort of further information. Obviously, he's a pretty tough cookie for him to come off, it must be sore, but yeah, look it's not ideal. But again it's another game where we've had to reshuffle our back line."
Romero had overcome a knock sustained in the midweek EFL Cup win over Manchester City to start against Villa, where Micky van de Ven watched on from the sidelines after his hamstring injury in that 2-1 last-16 victory.
With Van de Ven sidelined, Radu Dragusin - the only other recognised centre-half in Spurs' squad - partnered Romero from the first whistle, and the Romanian saw out the contest with Davies after his South American colleague was withdrawn.
Postecoglou will likely go with a Davies-Dragusin pairing against Galatasaray and Ipswich Town next week if Romero's problem proves serious, although 18-year-old Archie Gray played as a centre-back against Ferencvaros in the Europa League earlier this season.
Postecoglou explains early Son substitution in Villa win
Further up the field, Son started on the left-hand side after recovering from a hamstring problem, and the Spurs captain provided the assist for Johnson's equaliser before being taken off on the 56-minute mark.
Son seemed perplexed that his number was up, and the 32-year-old was visibly miffed as he took his seat on the bench, but Postecoglou insisted that it was always the plan to take him off around the hour mark following his recent layoff.
"He was never going to play more than that today because, obviously he had an injury, came back and last time it was around the 60 minute mark where he kind of got fatigued last time. So he was never going to play more than sort of 55/60 minutes irrespective of how the game was going," Postecoglou added.
"The great thing was that he made a pretty important contribution, before that, the great ball in for our first goal and we got our equaliser. So, you know, again, we got more battles ahead and we're going to need him. So he was never going to play more than that."
Tottenham's triumph has propelled them up to seventh in the Premier League table, just two points behind fourth-placed Arsenal, and Postecoglou's side now prepare to travel to Galatasaray for Thursday's Europa League showdown.