After this victory, tied for second, Spurs are finally out of the relegation zone, with a point more than city rivals West Ham who lost convincingly to Brentford yesterday. On the other hand, the Elves remain fifth (the place guaranteed by the Champions League) in the table with 58 points, the same as Liverpool, six more than Bournemouth.
Roberto De Zerni's team took the lead in the 12th minute through Conor Gallagher.
Richarlison increased the guests' advantage in the 25th minute.
Aston Villa's defeat was mitigated by Emiliano Buendia in practically the last attack of the match.
Tottenham welcomes Leeds in the next round, while Aston Villa takes on Burnley, who have long since been written off.