Graham Taylor's team completely dominated the rest of the match but wasteful finishing and good goalkeeping from Kasey Keller ensured they finished empty handed.
The visitors started brightly and after Teddy Sheringham headed over Christian Ziege's free-kick they had four good chances to take the lead. The first two fell to Lee Hendrie and the young midfielder was only inches wide on both occasions firing just over from 25 yards and then volleying narrowly wide two minutes later.
The next chance fell to Darius Vassell who shot just wide from 20 yards and then Keller was called into action to palm Peter Crouch's effort around the post.
With Villa so on top it was undeserved when Spurs took the lead and the goal came thanks to two new signings. Milenko Acimovic and Redknapp.
Mark Delaney handled on the edge of the area and Acimovic's fierce free-kick was parried by Peter Enckelman and with the goalkeeper still on the floor Redknapp very cleverly lofted a shot inside the far post.
It was harsh on Villa but they only had themselves to blame for not taking their chances and they spurned another two before half time with Crouch heading just wide and then Hendrie whipped a shot across the face of goal.
Taylor turned up the heat on the Spurs defence in the second half by bringing on strikers Juan Pablo Angel and Marcus Allback and switching Vassell to the right.
It proved a good decision as Vassell gave Ziege a torrid time and it was the England striker who gave Angel his first sight of goal only for the Colombian to shoot straight at Keller.
It was all one-way traffic but Villa just could not find the back of the net and it started to look like it was not going to be their day when Gareth Barry volleyed Alan Wright's cross towards goal only for Keller to palm the ball on to the post.
The best chance though came with 21 minutes to go when Vassell tormented the Spurs defence to give Angel a clear chance yet the striker hit his shot straight at Keller and Vassell blasted the rebound over the bar.
Villa kept pressing but that was their last real opportunity as Spurs held on for a hard fought win