The sides' first meeting since Germany's bruising 4-1 win in the last 16 at the 2010 World Cup in South Africa was decided by a 39th-minute header from Arsenal defender Per Mertesacker.
Spurs had just taken a 31st-minute lead through Andros Townsend at Villa Park when a canister trailing black smoke was lobbed towards the playing surface, apparently from the away supporters' section.
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.
Prior to this season Townsend, who had scored three goals in 18 Spurs appearances, had had loan spells at nine different clubs.
According to the reports, England manager Roy Hodgson encouraged his players to pass the ball to in-form Tottenham Hotspur winger Townsend by telling a joke about a monkey being sent into space by US space agency NASA.
The England manager said he is dreading the prospect of picking a 23-man squad for next year's World Cup in Brazil.
The 22-year-old winger was handed his first cap by manager Roy Hodgson and the gamble paid off as he settled the hosts' nerves with a late strike after the visitors had threatened to come back into the game.
The 32-year-old was replaced by Eden Hazard in the 75th minute of Chelsea's 3-1 win at Norwich City in the Premier League and was seen holding his side in apparent discomfort.
There is still a chance David Moyes will return with one more offer and Roberto Martinez admitted he would have preferred the window to close before the start of the season.
England play Moldova and Ukraine as part of the World Cup qualifiers next month.