The 22-year-old winger, who starred as England booked their place at the World Cup earlier this week, scored the opening goal with a 31st-minute cross that crept past Villa goalkeeper Brad Guzan.
Roberto Soldado added a second after half-time as Spurs moved up to fifth place in the table, three points below leaders Arsenal, and began to atone for their shock 3-0 home defeat by West Ham United.
It was a first defeat in four league games for Paul Lambert’s Villa, who now find themselves 13th, but it was a marked improvement on their 4-0 capitulation to the same side in the League Cup last month.
Villa had last season’s top scorer Christian Benteke on the bench following a hip injury, with Nathan Baker replacing Ciaran Clark in the only change to the side that drew 0-0 at Hull City last time out.
Spurs manager Andre Villas-Boas brought Lewis Holtby into his team in place of Christian Eriksen, awarded Vlad Chiriches his debut at centre-back, and handed Sandro a first league start since January.
Villa forward Gabriel Agbonlahor put a half-volley over the bar from an early Leandro Bacuna cross, but heavy rain made for a slippery surface and the game suffered as a result.
Linesman hit by flare
An assistant referee was struck by a flare thrown from the stands during the first half of the game between Aston Villa and Tottenham Hotspur. Spurs had just taken a 31st-minute lead through Andros Townsend when a canister trailing black smoke was lobbed towards the playing surface, apparently from the away supporters’ section. It hit the assistant referee, causing him to stumble forwards, but after a brief stoppage while referee Phil Dowd spoke to his colleague, the game continued.