Victory moves Spurs two points above their local rivals into eighth and keeps their chances of Europa League football next season alive, even if a return to the Champions League looks beyond them.
The loss was the first in six games for Arsenal, who drop to ninth, as old defensive frailties came back to haunt Mikel Arteta's men after an impressive spell.
Draws for both sides in midweek realistically ended any chance of Champions League football next season, even if Manchester City's appeal against a two-season ban from European competitions fails on Monday to pave the way for fifth place to qualify.
However, there was still the pride of north London to play for and plenty for both sides to prove ahead of a tight turnaround before next season.
Tottenham failed to even muster a shot on target in a dire 0-0 draw at relegation-threatened Bournemouth on Thursday that raised more questions over their direction under Jose Mourinho.
There was more urgency from Spurs from the off as Lucas Moura tested Emiliano Martinez inside the first minute.
Harry Kane had scored 10 goals in 11 previous derby appearances against Arsenal, but the England captain had a frustrating day in front of goal as he missed the first of a series of chances when he attempted to lob Martinez who anticipated and made another impressive stop.
Arsenal's impressive form in recent weeks put them in position to finish above Tottenham in the table for the first time in four years and they began to impose themselves on the game with Pierre-Emerick Aubameyang uncharacteristically wasteful from Hector Bellerin's cut-back.
The Gunners did go in front moments later in spectacular fashion as Alexandre Lacazette picked up a loose ball 25 yards from goal and blasted into the top corner for just his second league goal away from home this season.
Arsenal quickly undid that good work as Sead Kolasinac's wayward pass allowed Son Heung-min to outsprint David Luiz before coolly chipping the ball over the onrushing Martinez.
Both sides came close to scoring again before half-time as the action mirrored a pulsating 2-2 draw at the Emirates earlier in the season, even if there was not the atmosphere synonomous with a derby.
Tottenham left-back Ben Davies crashed a long-range effort off the bar before Nicolas Pepe curled an effort inches wide at the other end.
With Arteta audibly orchestrating his troops from the sidelines, Arsenal controlled long spells of the second half, but failed to make their pressure count.
Aubameyang smashed the visitors' best chance off the crossbar before he was denied again by Hugo Lloris flying low to his left to turn the ball behind for a corner.
Spurs were always a threat on the counter-attack. Martinez had to be quick off his line to deny Son a tap in for his second after Kane outmuscled Shkodran Mustafi.
Kane was then denied once more by the Argentine goalkeeper from a narrow angle, but from the resulting Son corner, Alderweireld leapt highest to head into the far corner.