Andros Townsend capped a fine week as the England winger and Roberto Soldado struck to down Villa.
The 22-year-old, who helped England qualify for the World Cup, scored when his first-half cross dropped in to give Tottenham a fortuitous lead.
Soldado killed off any hopes of a Villa fightback with a superb second as Spurs took control after Townsend’s opener.
Christian Benteke returned after a month out with a hip injury and missed a golden chance to equaliser just before Spurs’ second.
But Tottenham's win was marred after linesman David Bryan was hit by a flare thrown from the away end as they celebrated the first goal.
There was confusion over Villa’s selection before kick-off but Benteke was named on the bench and Nathan Baker replaced Ciaran Clark in Villa’s only change from the 0-0 draw at Hull two weeks ago.
Gabby Agbonlahor fired over after three minutes when Michael Dawson failed to clear Leandro Bacuna’s cross in a bright start.
Ashley Westwood was booked for a rough challenge on Lewis Holtby as Villa pressed and contained the visitors.
But they fell behind on 31 minutes when Townsend tossed in a dangerous delivery and it missed Holtby and Soldado to drop into the far corner with Guzan statuesque.
It was harsh on Villa and it killed their momentum as Tottenham began to dictate the play. Bacuna fired a free kick over and Andi Weimann shot wide as the hosts tried to rally.
But Guzan denied Townsend a second with a smart low stop in first half injury time.
The England winger shot over just after the break before Benteke returned on the hour, replacing the quiet Kozak.
And he should have scored three minutes later when he headed Bacuna’s cross over from seven yards.
Six minutes later it was 2-0 when Holtby and Paulinho sliced through Villa’s defence to set Soldado up to fire past Guzan from 10 yards.
With Spurs comfortable they created more chances with Paulinho heading at Lloris and Townsend firing over.
Aleksandar Tonev went close twice but Villa failed to mount a recovery.