Arsenal took the lead just before half-time through unlikely goalscorer Per Mertesacker.
The big German centre-half connected with a whipped corner from Granit Xhaka to head the Gunners in front on 39 minutes.
But Watford were never out of it and were rewarded for their endeavours on 70 minutes with a penalty after Hector Bellerin brought down Richarlison.
Substitute Troy Deeney stepped up to take the spot-kick and dispatched it with ease, sending Petr Cech the wrong way.
The home side came close to sealing all three points on 82 minutes as Etienne Capoue saw an effort deflect off Mertesacker and strike the post.
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But the Hornets did snatch the win in added time as Tom Cleverley lashed home the ball in the 18-yard box to make it 2-1.
The result sees Marco Silva’s side move up to fourth in the Premier League table, leapfrogging the Gunners who drop to sixth.