The Hornets found themselves two goals up inside the opening 13 minutes and, despite seeing their opponents pull one back before the hour, successfully saw things through.
Victory for Watford - their first in eight league games - is a huge blow to Arsenal's Premier League title hopes, as they missed out on the chance to close the gap on league leaders Chelsea.
It was another foe of the Gunners', Etienne Capoue, who created the second after making good inroads through a non-existent Arsenal midfield and defence.
The Frenchman was allowed to waltz through on goal only to see his shot kept out by Cech, but Troy Deeney found himself well positioned to score from the rebound.
Watford had never previously scored a Premier League goal at the Emirates Stadium and had never led in a Prem game against their London rivals, but a storming start to the match put that right.
It was certainly a shock to the system for the Gunners, who had not shipped a goal inside the opening 15 minutes all term prior to this evening, and they struggled to find any sort of rhythm in the remainder of the first half.
Under-fire Watford boss Walter Mazzarri would have been disappointed to see his charges go into the interval with just a two-goal advantage, in fact, as Cech did well to keep out on-target attempts from Capoue, Sebastian Prodl and Daryl Janmaat.
The visitors were bullying their opponents at times, winning all the 50-50 challenges which inevitably led to jeers as Arsenal - correctly denied a penalty when Nacho Monreal went to ground under minimal contact - made their way off the field for half time.
Not since 2001 have Arsenal recovered from two goals down to win a home league match and, with matters made worse due to an injury picked up by Ramsey, touchline-banned boss Arsene Wenger turned to fit-again Theo Walcott for the second half.
It almost paid instant dividends for the hosts, as the Englishman blasted behind from his first meaningful touch and was then thwarted by Heurelho Gomes from close range.
Gomes has conceded more goals against Arsenal than any other opponent faced in his career, but he was doing his best to hold off the onslaught by denying both Alex Iwobi and Mesut Ozil in quick succession.
The Arsenal dominance finally told just short of the hour mark, though, as Sanchez - moments after seeing a penalty appeal of his own turned down - worked his way into the box down the right and sent the ball across for Iwobi to trickle over the line.
Wenger's men could not sustain quite the same level of dominance after finally finding a route back into the game, sending shots wide through Gabriel Paulista and Monreal over the next 20 minutes.
No team has scored more goals in the final 10 minutes of a game than Arsenal this term, but a Lucas Perez strike against the crossbar proved to be the closest they came to a leveller, ending their 10-game run without defeat here.