The Gunners took the lead on eight minutes when Shkodran Mustafi headed in from a Mesut Ozil free-kick, his 50th assist in the competition.
Just before the hour mark, Henrikh Mkhitaryan played in Pierre-Emerick Aubameyang, who rounded Watford goalkeeper Orestis Karnezis to score the second.
The visitors had a great chance to get a goal back but Cech saved Troy Deeney's penalty. Arsenal sealed victory when Mkhitaryan scored from the edge of the area with 13 minutes left to play, his first goal in the PL for the Gunners.
Arsenal's first win in four PL matches means they remain in sixth, eight points behind Chelsea in fifth, while Watford drop to 10th place.
Arsenal: 1 Apr v Stoke City (H)
Watford: 17 Mar v Liverpool (A)