With Spurs set to play to Wembley next season ahead of their planned move to their new stadium for the 2018/19 season, Mauricio Pochettino's side signed off in style with a comfortable win.
Alli reacted quickest to a save from the impressive Petr Cech to put Spurs ahead 10 minutes after half-time, and Kane teased Gabriel into conceding a penalty two minutes later before dispatching the spot kick to seal the win.
Tom Collomosse assesses the key talking points for Spurs...
Spurs fans take time to find their voice
The atmosphere was good, of course - yet before the opening goal, it lacked the sharp edge of most north London derbies here.
This was surely because nearly all home supporters were aware of Chelsea’s victory at Everton earlier in the afternoon.
Had the Premier League leaders dropped points at Goodison Park, Tottenham would have closed the gap with a win over Arsenal.
Yet Chelsea’s 3-0 win meant Spurs required three points here just to keep the Blues’ advantage to four points.
However much Tottenham wanted to beat Arsenal, their fans were also dreaming of the title. By kick-off time, those hopes had faded considerably.
Mousa not missed
Mousa Dembele has been one of Tottenham’s most influential players this season, so when an ankle problem meant he was named only among the substitutes, Arsenal would have felt encouraged.
Yet the performances in the centre of Eric Dier and Victor Wanyama were so strong that Dembele’s absence was barely noticed.
Dier prefers midfield to defence, but has had few chances there due to the Wanyama-Dembele axis - which is why Manchester United believe they may be able to sign him for £40million in the summer.
Wanyama was perhaps even better, contributing brilliantly in both attack and defence to ensure Tottenham controlled most of the game.
What now for Walker?
Tottenham have played Chelsea and Arsenal in the space of eight days, and Kyle Walker has started neither match.
However Tottenham choose to present it, this is a worrying situation for a player many believe to be the best English right-back.
Walker has become unsettled recently, holding talks with manager Mauricio Pochettino amid suggestions that Manchester City are prepared to double his £70,000-a-week salary.
Walker played poorly in the 1-0 win at Crystal Palace in midweek and against Arsenal, his replacement Kieran Trippier did a solid job.
If Trippier stays in the team for the rest of the season, does that mean Spurs are thinking about selling Walker?
No St Totteringham’s Day in 2017
For the first time since 1995 – when Christian Eriksen was three, Harry Kane one and Dele Alli not yet born – Tottrenham will finish above Arsenal in the Premier League.
Barring a huge swing in goal difference, Tottenham will also play Champions League football next term. They have 77 points and a goal difference of +49 with four games remaining.
Fifth-placed Manchester United have 65, meaning they must win all their remaining games and improve dramatically their +26 goal difference in the process.
Even if - as appears probable - Spurs do not win the title, they still have much to celebrate from their final season at White Hart Lane.
Davies shows his quality
Most of the credit for this victory, in the final north London derby at White Hart Lane, will inevitably go to goalscorers Dele Alli and Harry Kane, and manager Pochettino.
Yet the contribution of Ben Davies should not be overlooked. Davies may lack the dynamism of Danny Rose, who is still absent through injury but he has rarely let his team down since Rose damaged medial knee ligaments in the 0-0 draw at Sunderland on January 31.
Tottenham’s results have been excellent since, suggesting Davies has done his job well. He was excellent against Arsenal, keeping Mesut Ozil quiet and ensuring Alex Oxlade-Chamberlain rarely threatened. On top of this, he was always available in attack