Johan Manzambi put Villa in front in the third minute of first-half stoppage time, with Tottenham briefly down to ten men while Micky van de Ven had treatment for a cut under his eye. Nicolas Jackson made it 2-0 on 67 minutes with a low finish after Manzambi's assist, and Emiliano Buendía curled in a third on 79.
Conor Gallagher scored Spurs' first Premier League goal of the season on 86, and Jan Paul van Hecke headed a second in the eighth minute of stoppage time.
Unai Emery, speaking to VillaTV, was delighted with the response.
"We are delighted (with) how the players responded on the field (with) the gameplan we planned, how we were needing (to) get points and in this stadium, in this scenario, against Tottenham away, it's always being very difficult.
"But we competed fantastic. We were defending collectively strong the first half. We needed the 'keeper, we needed (to) defend a lot of corners defensively and we were resilient."
Roberto De Zerbi would not dwell on a dominant first half.
"I don't want to speak about the first half when we dominated the game, we create more chances to score, we play well. I don't want to speak because my focus is why we concede the first goal with 10 players, just for one minute in that situation. We can stay stronger, we can communicate more and more and more, we can defend in a compact way."
He was critical of the second goal.
"I don't know if some players lost energy, but we conceded an unacceptable goal from a long goal kick, with a long ball.
"Today I was very disappointed, very sad, very frustrated for the performance. Because we can't lose this game, in this way, absolutely. We can't concede the second goal."
Asked about striker Dominic Solanke, De Zerbi backed him.
"We need more from him, for sure, but he's one of my players. I like Dom as a player, and I stay with him until the end."
Emery finished by thanking the travelling supporters.
"But today, very good, and of course, the supporters as well, passion. I am so, so happy and very proud of how we did the work, but of course, as well because they are with us."
Villa have won eight of their last 11 meetings with Spurs in all competitions. Villa's next league game is Brentford, after the international break.