Jermain Defoe scored once in the first half and again in injury time, with Paulinho also netting, though the hosts wanted a penalty for a peculiar challenge by Jan Vertonghen
Defoe – who netted twice on his last appearance for Spurs against Tromso – headed his side into the lead on the stroke of halftime after great work from Lewis Holtby at Villa Park on Tuesday.
Paulinho doubled Tottenham's lead with a near-post flick just four minutes after the break and substitute Nacer Chadli sealed the win with a powerful late finish.
There was still time for Defoe to get a second goal though, as he rounded Villa goalkeeper Jed Steer in stoppage time to score his sixth goal of the season.
Both sides rang the changes, with Villa making seven, as striker Libor Kozak was handed his first start in the absence of the injured Christian Benteke (hip).
Tottenham made eight alterations, as Defoe returned from a niggle, while Romanian defender Vlad Chiriches made his long-awaited debut after finally receiving his work permit following his move from Steaua Bucharest.
In a first half dominated by Tottenham, Harry Kane, Defoe and Erik Lamela all had early attempts on goal but, at the other end, visiting goalkeeper Brad Friedel got down well to deny Marc Albrighton with a smart save.
Defoe had two more efforts on goal as Tottenham pressed, while Albrighton shot over, before the hosts stepped up the pace 10 minutes before the break.
First, a flowing counterattack involving Lamela and Holtby saw the former’s shot well saved by Steer, who was also called upon to keep out a placed Defoe effort.
Tottenham deserved a goal for their dominance and it got it on the stroke of the interval, as Defoe played in Paulinho, who flicked to Holtby.
The Germany international lobbed a sublime ball into the area and Defoe – who had continued his run – nodded beyond the reach of Steer.
Villa made two changes at the break, as Nicklas Helenius and Jordan Bowery were introduced in place of Kozak and Karim El Ahmadi, and one of boss Paul Lambert's additions almost made an immediate impact.
Helenius beat Tottenham's Jan Vertonghen to a long ball, before closing in on goal, only for the Spurs defender to bizarrely pull his shorts down as they tangled, with the eventual shot going wide.
Lamela had a free kick deflected just wide shortly afterwards, and from the resulting corner Tottenham increased its advantage, as Paulinho charged to the near post and acrobatically flicked Holtby's cross into the net.
Paulinho had another effort saved while Kane saw a shot deflected wide, and Aleksandar Tonev forced a good save out of Friedel with a well-hit strike.
But Chadli and Defoe wrapped up the win for Tottenham in the dying stages, with the former beating Steer at his near post before Defoe rounded the Villa goalkeeper and scored an easy tap-in.