Tottenham drew level on points with second-placed Manchester United, just three behind leaders Manchester City, after comfortably beating Everton.
The hosts suffered an early scare when Louis Saha fired wide, but took control and opened the scoring when Aaron Lennon cut in from the left to slot in.
Emmanuel Adebayor shot over and wide as Spurs created a number of chances.
However, pressure on the Everton goal finally told when Benoit Assou-Ekotto smashed into the corner from 30 yards.
The visitors did have a penalty appeal waved away by referee Martin Atkinson when Younes Kaboul tripped Royston Drenthe late on, but David Moyes's team suffered a fruitless evening in the capital and defeat continued their indifferent form.
Redknapp pleased with clean sheet
This game was the rearranged fixture after the original game was postponed because of the London riots.
And although Spurs suffered a sticky start to the season following defeats by their title rivals, they will be grateful to finally reduce the gap at the top to put them firmly in the Premier League title race.
Once Saha shot off-target following Kaboul's poor clearance, Spurs were dominant and should probably have taken the lead before they did.
Adebayor was the guilty party on several occasions, blazing over from a tight angle and then poking wide when the ball broke to him from an Assou-Ekotto cross.
He also mis-controlled a pass after a good break by Rafael van der Vaart and Gareth Bale, with Tim Howard putting him under pressure.
Victory over Everton earned Spurs their eighth clean sheet of the season, the same total as the whole of last season
Some of the hosts' passing and movement was a joy to watch at times, with Luka Modric ably supported by Jake Livermore, who was starting in place of the injured Scott Parker.
Van der Vaart curled the ball over before the half hour point and just as it looked like they might draw a blank in the first period Lennon broke the deadlock with his fourth of the season.
Assou-Ekotto pinged a long diagonal ball out to the right-winger, and with Leighton Baines losing the ball in its flight, the England player dribbled inside and shot left footed past Howard as the Everton defence tried to block his shot.
Coming into the game, the visitors had lost just once to Tottenham in their last eight league games, but they were soon under pressure in the second period as a marauding Bale run and shot was well saved by Howard.
Soon after, there was another isolated opportunity for Saha but his shot at the near post following Baines' centre, was deflected wide.
Moyes satisfied despite defeat
Marouane Fellaini headed over, too, in a sure sign that David Moyes had asked for an improvement at half-time.
But any hope of building on that was soon knocked into touch as Assou-Ekotto doubled the lead with a glorious strike. With little in front of him, the Cameroon international received the ball square and smashed a shot into the corner from 30 yards, although it did take a touch off Tim Cahill as it flew in.
Having set up the first goal, the Spurs left-back enjoyed a profitable night and only more waywardness by Adebayor and Bale meant the scoreline did not increase.
Drenthe's penalty appeal was the only late glimmer that Everton could muster on a disappointing night.
But having won 14 of their 20 league games so far and sitting level on points with Manchester United, Tottenham will care little as they build their title challenge.
Following this performance they may now relish the trip to Manchester City on 22 January.
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