The game had been breathless but low on quality in front of goal until Arsenal punished Spurs from a corner, having done so twice in last season’s 3-2 away win in April.
Gabriel escaped far too easily from Cristian Romero, who pleaded for a foul in vain, and powered a header past Vicario from close range in the 64th minute.
Arsenal withstood some late pressure from Spurs, who created few real chances and were left shooting from range as the Gunners seemed happy with a one-goal lead.
The win, their third in a row away to their bitter rivals, puts Arsenal on 10 points from four games, two behind champions Manchester City ahead of their trip to the Etihad next Sunday.
Arsenal first play Atalanta away in the Champions League on Thursday and will hope Saka, who was substituted late on, can recover in time to play a part.