Arsenal went in front in the 16th minute through Alexandre Lacazette’s stunning strike into the top-left corner from 20 yards.
Their lead lasted just 70 seconds, as Son Heung-min latched on to a loose pass by Arsenal’s Sead Kolasinac and lifted the ball over Emiliano Martinez.
Both sides hit the woodwork either side of half-time. Ben Davies’s strike from distance was tipped on to the bar by Martinez, while Pierre-Emerick Aubameyang’s fierce shot came off the corner of the goal after the break.
The decisive moment came with nine minutes remaining, when Alderweireld headed in from Son’s corner.
Spurs move above Arsenal into eighth with 52 points, three behind sixth-placed Wolverhampton Wanderers.
Arsenal are ninth, two points behind Spurs.
Arsenal.boss, Mikel Arteta said: “We are really, really sad. I am really proud of the players. But we give them a goal again and we concede from a set-piece. You cannot do that at this level. The game was ours and we had complete control. It’s difficult to attack a low block like this but the small details have cost us. That’s where we have to improve as a team.”
Tottenham. Manager, Jose Mourinho was more upbeat.” The game was more tactical than anything else”, he said. “Mikel found a way for them to play and be stable – they are improving. We felt we should adapt slightly to them and we did it very well. We had great spirit and fought really hard considering Arsenal had 48 hours more than us to rest. This effort came from their hearts. We are happy because we’ve made the fans happy and we’re still in the fight for the Europa League positions.”