Per Mertesacker marked his first Premier League start in 532 days with the opening goal, the defender converting Granit Xhaka's corner in the 39th minute, to put Arsene Wenger's side on course for a fifth successive win in all competitions.
A 71st-minute equaliser from the penalty spot by substitute Troy Deeney got the hosts on level terms and set up a thrilling finish.
After Etienne Capoue hit the post, the game appeared set to finish all-square until Tom Cleverley popped up with an injury-time winner, completing the recovery mission and sending Watford above Arsenal and up to fourth in the table.
90 - Arsenal have lost to a 90+ minute winner in the Premier League for the first time since January 2012 (Bobby Zamora for Fulham). Stung.— OptaJoe (@OptaJoe) October 14, 2017
Cleverley - who had been easily beaten in the air for Mertesacker's header - was in the right place in the penalty area to convert a loose ball, meaning the Gunners are still yet to record an away league win this season.
The dramatic finish spectacularly bursts the fragile bubble of optimism that had been growing at Arsenal, who had put together an impressive run of form since a 4-0 hammering at Liverpool on August 27.
Wenger will rue his side's failure to hold onto a lead given to them by the most unlikely of goalscorers, club captain Mertesacker - who replaced the injured Shkodran Mustafi in the starting XI - celebrating a rare outing by breaking the deadlock with his side's first away goal in the league since May.
The set-piece effort came after Arsenal had struggled to break down a Watford side that mirrored their opponents by starting with a three-man back line, the visitors too often settling for long-range attempts or throwing in hopeful crosses.
Silva switched to 4-4-2 on the hour mark and the move paid off when club skipper Deeney - without a goal in his previous 13 league games - matched his Arsenal counterpart by converting from the spot after Hector Bellerin was adjudged to have pulled down Richarlison.
12 - Petr Cech has failed to save any of the 12 penalties he has faced with Arsenal in all competitions. Rooted. pic.twitter.com/7uZyt9EOXp— OptaJoe (@OptaJoe) October 14, 2017
The equaliser came after Arsenal had twice fluffed their lines at the other end.
Alex Iwobi and the fit-again Mesut Ozil, on as a replacement for the injured Danny Welbeck, were both guilty of putting ione-on-one attempts too close to goalkeeper Heurelho Gomes, letting Watford off the hook.
The closing minutes saw Arsenal come under siege, with the post helping them out when Capoue's first-time drive from Deeney's pass struck Mertesacker's chest and wrong-footed Petr Cech.
However, the woodwork failed to come to their rescue again when Cleverley arrived at the perfect time to slam home a dramatic winner three minutes into added time.
Key Opta stats:
- Watford have 15 points already this season, their best tally after eight top-flight games since 1982-83, when they managed 16 points under Graham Taylor.
- Per Mertesacker scored his first Premier League goal in 1400 days, since netting v Manchester City in December 2013.
- Cleverley's goal was his first in a league game for Watford since March 2010, when he netted against Sheffield Wednesday in the second-tier.