Mustafi's header came after referee Mike Dean had awarded a dubious free kick for a foul on Sanchez while Alexandre Lacazette was just offside in the build-up to their second.
But few could argue with the result as Arsene Wenger's side beat Tottenham at their own game, showing themselves faster, stronger and hungrier than their opponents in every department.
Ben Davies seemed a particular target, with several openings coming down Tottenham's left, as Hector Bellerin and Mesut Ozil both fired dangerous balls across the box.
Christian Eriksen, virtually anonymous until this point, clipped the post with a dragged shot but it was no surprise when Mustafi headed Arsenal in front in the 36th minute.
Lacazette's arm looked on replay to have just been offside and Spurs assistant Jesus Perez waited to give Dean an earful in the tunnel at half-time.
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