Villa remain bottom of the table after their seventh straight Premier League defeat, and despite showing the fight for a battle against relegation they need a dramatic turn around after taking only four points from their first 11 games
Mousa Dembele fired Tottenham ahead after only three minutes and Dele Alli made it 2-0 on the stroke of half-time
Villa surprisingly pulled one back when Jordan Ayew's 79th minute shot was deflected but a fine strike from Harry Kane in stoppage time made sure of the win for Spurs
Garde's was a watching brief only with the match kicking off hours after he took charge, while Villa captain Micah Richards learned shortly before kick-off that he was suspended after admitting a misconduct charge from the Football Association relating to the loss against Swansea.
Without their skipper, Villa started poorly
As if to highlight their many struggles, Spurs' Mousa Dembele collected a third-minute pass from Danny Rose on the left wing before cutting inside to the penalty area, easing past Ciaran Clark - starting in Richards' absence - and sending a left-footed shot through Brad Guzan's legs
For a team so obviously bereft of confidence it seemed likely to be only the first of several goals that would soon follow, but after a flat period Villa impressed in their initial reaction, even if it came amid Spurs' casual approach
The lively Scott Sinclair, who in unison with Jack Grealish can form the start of a promising attack, dribbled inside from the left wing before sending a powerful shot at Hugo Lloris which the goalkeeper routinely saved.
It took until the 24th minute for Spurs to again threaten, this time when Harry Kane created space before his close-range shot was deflected by Alan Hutton and impressively tipped over by Guzan, and shortly before Dembele's 25-yard strike comfortably cleared the crossbar.
Spurs had relaxed amid the security provided by their early goal, but they again began to demonstrate their superior quality and in the first minute of first-half stoppage time the impressive Alli - in front of the watching Roy Hodgson - doubled their lead.
Joleon Lescott's loose header fell his way and the talented 19-year-old showed a maturity beyond his years to tee up his right-footed shot and find the bottom-left corner.
Villa caretaker manager Kevin MacDonald responded at half-time by introducing Rudy Gestede but the striker continued his Premier League struggles and was never likely to inspire a comeback.
Instead, Spurs' uncharacteristic sluggishness left an opening.
Leandro Bacuna had already struck the post when Ryan Mason gifted fellow substitute Jordan Ayew possession in midfield, and the forward ran into space before striking a shot which deflected off Toby Alderweireld, beyond Lloris and into the bottom left corner.
Ayew immediately threatened with another effort from midfield, but as Villa pushed forward they gifted space to Spurs
Christian Eriksen and Erik Lamela used it to set up Harry Kane, who with time and space effortlessly curled into the top right corner.
The result not only consigned the visitors to further misery, it also meant their worst start to a top-flight season since 1919
TWEET OF THE MATCH
"Well how good was that 3-1 to Spurs
Play the kids on Thursday as we need to stuff Arsenal
If we do that we are contenders for 4th" - Tottenham fan Lord Sugar (@Lord_Sugar) is willing to risk losing points against Anderlecht in the Europa League to ensure Spurs are fresh for the north London derby.
HUGO LLORIS: 7 (out of 10)
KYLE WALKER: 6
DANNY ROSE: 5
TOBY ALDERWEIRELD: 7
JAN VERTONGHEN: 6
ERIC DIER: 5
DELE ALLI: 7
MOUSA DEMBELE: 7
CHRISTIAN ERIKSEN: 7
ERIK LAMELA: 6
HARRY KANE: 7
RYAN MASON (for Dembele, 69): 5
BEN DAVIES (for Rose, 82): 6
JOSH ONOMAH (for Alli, 90): 5
BRAD GUZAN: 7
CIARAN CLARK: 5
LEANDRO BACUNA: 5
SCOTT SINCLAIR: 6
GABBY AGBONLAHOR: 5
ASHLEY WESTWOOD: 6
JOLEON LESCOTT: 6
KIERAN RICHARDSON: 5
ALAN HUTTON: 6
CARLOS SANCHEZ: 5
JACK GREALISH: 7
JORDAN AYEW (for Westwood, 38): 7
RUDY GESTEDE (for Agbonlahor, 45): 6
CARLES GIL (for Grealish, 65): 7
Dele Alli: It was hardly a game for outstanding individual performances but Alli was dynamic with his runs and capped another impressive display with a well-taken goal on the stroke of half-time.
MOMENT OF THE MATCH
Ayew's long-range strike came out of the blue for Villa in the 79th minute and set up a nervous finish at White Hart Lane
The young forward has struggled to settle since arriving at Villa Park in the summer but new boss Remi Garde will hope this goal can spark a better run of form for the 24-year-old.
VIEW FROM THE BENCH
Garde was watching on from the stands and he will have learned a great deal from his side's defeat
Villa are struggling for goals and that showed, with neither Rudy Gestede nor Gabby Agbonlahor offering much threat before Ayew's deflected second-half strike
Mauricio Pochettino would have liked a more comfortable win for Spurs, particularly with Anderlecht to come on Thursday in the Europa League before a visit to Arsenal on Sunday
As it was, Spurs were left hanging on before Harry Kane completed the win in injury time.
MOAN OF THE MATCH
Why was Ayew not starting? The forward looked bright when he came on and surely needs to be given more games, and confidence, under his new manager.
WHO'S UP NEXT
Tottenham v Anderlecht, November 5 (Europa League)
Aston Villa v Manchester City, November 8 (Premier League)
Source : PA