Hugo Lloris made his home league debut and Tottenham occasionally looked vulnerable at the back, but were in control for the vast majority of the game and played some of their best football of the season.
Birthday boy Jermain Defoe, Jan Vertonghen and the mightily-impressive Gareth Bale all came close to putting Spurs ahead in the first half, but the Londoners only broke the deadlock after the break through Caulker's lucky first goal for the club.
Defoe smashed a low shot wide from a Bale corner, but the defender was standing in the right place at the right time, the ball clipping his heel and flying past Brad Guzan after 58 minutes.
Soon after Spurs put the game to bed when Lennon picked the ball up off Dempsey, strode past his marker and shot beyond Guzan.
Manager Andre Villas-Boas made the surprise decision to end Brad Friedel's run of 310 consecutive Premier League starts by giving Lloris his English top-flight debut.
The Frenchman, signed for £8million on deadline day, looked solid for the majority of the first half and barely had a thing to do after the break.
He did not hesitate to come off his line - a criticism often aimed at Friedel - and he will be glad to have been in goal for Spurs' first clean sheet of the season.
His only hiccup came just after the break when he threw a wayward ball to Vertonghen, but Villa failed to take advantage and Spurs ended the game full of joy knowing they had moved back up to fifth in the table with the win.
Lloris received a hero's welcome when he emerged from the tunnel, but he barely had anything to do for much of the opening quarter as Spurs started well.
With less than 30 seconds gone Defoe laid the ball off to Bale, who flashed a curling shot just wide.
Vertonghen then burst down the left flank and cut the ball back but Defoe blazed the ball over from 12 yards.
Bale whipped in a devilish cross after five minutes, but Vertonghen mistimed his run by a second and just missed a tap-in from close range.
Moments later Bale beat the offside trap and went to ground after rounding Guzan. The Welshman appealed for a foul which would have seen the American red-carded, but referee Neil Swarbrick waved play on.
Lloris' first piece of action came after 20 minutes when he saved awkwardly from Christian Benteke, but the Frenchman showed confidence by racing out to clear before Brett Holman could shoot.
Spurs were on top, but still could not find a way through.
Defoe gained a yard on his marker after picking up a Lennon pass, but he could only shoot a yard wide.
Lloris then did well to race out and deny Benteke and Gabriel Agbonlahor in quick succession as Villa threatened to score on the counter.
Tottenham failed in their bid to break the deadlock before the break - and they almost went behind just after the restart thanks to Lloris' only error.
Villa intercepted the Frenchman's throw to Vertonghen and Agbonlahor found the unmarked Benteke at the back post but he headed wide.
The crowd, fully aware of the cost of Spurs' profligacy against Panathinaikos on Thursday, became tense, but their nerves eased when Defoe's deflected shot went in just before the hour.
The England striker got on the end of Bale's cross and took a touch before firing a low shot that was going wide until it clipped Caulker's heel and flew past Guzan.
Nine minutes later it was 2-0 thanks to Lennon's first of the season. Joe Bennett failed to close down Dempsey, who squared for Lennon and he swept a precise shot past Guzan in to the far corner.
Villas-Boas brought on Emmanuel Adebayor for his first appearance in over a month.
Dempsey should have put the game beyond doubt 15 minutes from the end, but he somehow missed a free header from eight yards.
Worryingly for Villa, Bennett was carried off on a stretcher with 12 minutes left after clattering in to the advertising boards.
Bale lashed a powerful drive inches wide of a sprawling Guzan and the American did well to push Dembele's shot on to the bar near the end.