Jose Mourinho's charges put up a defensive masterclass as the Portuguese registered his first north London derby win and the first one to be played at the new Tottenham stadium.
Alexandre Lacazette's thunderous strike had given Arsenal an early lead in the 16th but the Gunners' defensive frailties came back to haunt them as Sead Kolasinac's error gifted Heung-Min Son the equaliser three minutes later.
Toby Alderweireld gave the hosts the victory when he rose highest to head as Arsenal defence, once again, guilty of ball watching.
Spurs started the match brilliantly with Lucas Moura testing Arsenal keeper Emiliano Martinez with a 30-yard stinger just after 30 seconds.
Martinez was again called on to save Arsenal from going behind 11 minutes later when he launched himself high into the air to stop a Harry Kane lofted finish.
At the other end, Pierre-Emerick Aubameyang spurned a glorious chance to hand Arsenal the lead when he swiped at thin air while attempting to convert Hector Bellerin's cross. Moments later Lacazette profited from Serge Aurier profligacy to unleash a venomous strike beyond a diving Hugo Lloris.
Spurs response was swift and effective as a poor Sead Kolasinac back pass found a willing Son who held off David Luiz before chipping over Martinez.
Aubameyang's half volley forced a fingertip save from Lloris as Arsenal pushed for a late winner, but they were undone with nine minutes remaining as Alderweireld rose high to head Son's corner home to maintain Mourinho's imperious home record against the Gunners.
The victory lifts Spurs above Arsenal into eight in the table, while Arsenal drop to ninth, two points adrift of their rivals with three games remaining.
Recap the Tottenham v Arsenal match updates and stats here.