For the Gunners that aim was winning the Premier League title, which now appears an unlikely outcome given that league leaders Chelsea are six points clear of Arsenal with four games to play.
For Spurs, however, fourth place in the Premier League and qualification for the Champions League remains a realistic aim with Redknapp's side one point behind fourth-placed Manchester City.
Both sides went into the north London derby viewing it as the perfect opportunity to put elimination from knockout competitions behind them.
Spurs had suffered a 2-0 defeat by Portsmouth in the FA Cup semi-final at Wembley on Sunday, while Arsenal's last game was a 4-1 loss to Barcelona at the Nou Camp which ended their Champions League campaign.
But it was Tottenham, without the benefit of an eight-day break, who played with more desire.
Redknapp sprung a surprise in his starting line-up, throwing Rose into the fray - and that decision was to reap dividends after 10 minutes.
Redknapp hails 'wonder goal'
Almunia punched away a corner but 30-yards out Rose was lurking and the 19-year-old unleashed an instinctive left-foot volley beyond the Arsenal keeper for one of the goals of the season.
Tottenham have only conceded 10 league goals at home this season, fewer than any other club in the division.
And Arsenal, unbeaten in their last eight league games, found the home side's back line tough to break down, struggling to create clear-cut opportunities despite dominating possession.
It was Spurs who started to ask questions of Arsenal's unconvincing defence, by now weakened after Thomas Vermaelen limped off with a calf injury to be replaced by Mikael Silvestre.
Almunia thwarted Luka Modric bravely before Defoe's snap-shot slammed into the body of the Spanish goalkeeper as Spurs pressed for a second goal.
And only one minute into the second half Spurs stunned Wenger's title-chasing side.
Defoe rode two challenges before splitting the Gunners' defence with a diagonal ball to the edge of the six-yard box where Bale, being played onside by Bacary Sagna, stroked the ball home with ease.
Shell-shocked Arsenal eventually regained their composure and tried to pick a hole in the Spurs back line but clear-cut opportunities were in short supply.
With the Spurs centre-back pairing of Ledley King and Michael Dawson proving almost impossible to break down, Wenger threw on Robin van Persie for his first game since rupturing ankle ligaments five months ago.
Title very unlikely now - Wenger
And the Dutchman made an impressive impact, forcing a stunning save from Gomes as the Gunners manically searched for a goal.
Van Persie took the ball on his chest on the penalty spot and swivelled quickly to crash a volley towards goal but Gomes instinctively palmed the effort over the bar.
And the Brazilian denied Van Persie for the second time in two minutes when he got his outstretched hand to the striker's vicious curling free-kick to turn it around the post.
The keeper completed a hat-trick of superb saves when he tipped Sol Campbell's header on to the crossbar.
However, tired legs which had defended manfully for Spurs finally faltered as Arsenal pulled back a goal to set up a tense finale.
Theo Walcott's low cross was met by Bendtner, who stabbed home from three yards.
But despite unrelenting Arsenal pressure in the four minutes of added time at White Hart Lane, Spurs held out for an impressive victory.
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