Spurs were next to threaten, and again it was a set piece that Dawson was unable to reach.
Their goal came soon after that incident, though, and it was Andros Townsend who continued his positive start to the season with a cross that missed everyone in the box and went in at the far post.
It was nearly 2-0 for Spurs, but Gylfi Sigurdsson missed with a header from eight yards out.
Andreas Weimann then shot wide for Villa, but Guzan was required to push away Townsend's shot just before half time.
Guzan was again at the heart of the action at the start of the second half, saving Paulinho's low shot.
Christian Benteke then went close for Villa but could not keep his header down.
Spurs made Villa pay for that miss as Roberto Soldado beat Guzan after being played in by Paulinho.
Andre Villas-Boas's team had two chances to extend their lead, as first Townsend flashed a shot over the bar and then Paulinho missed the winger's cross.