The Hornets raced into a 2-0 lead inside 15 minutes with a strike from Younes Kaboul followed up by Troy Deeney's effort. The Gunners cut the deficit with a goal on 58 minutes from Alex Iwobi but were unable to equalise as the Hornets claimed a famous win.
Crystal Palace remain in the bottom three despite securing a 2-0 win over Bournemouth.
The Eagles went ahead with a strike from Scott Dann two minutes after half-time before Christian Benteke wrapped up the points late on.
The Clarets rose to tenth in the standings after Sam Vokes struck the winning goal in the 87th minute.
Middlesbrough are also on the fringes of the drop zone despite coming from behind to secure a 1-1 draw against West Bromwich Albion.
Both goals came early in the game with the Baggies taking the lead inside six minutes through James Morrison but they were soon pegged back by Alvaro Negredo's penalty in the 16th minute.
The goalless draw benefits the hosts more than the visiting Spurs who missed the chance to cut the gap to Chelsea at the top.
Swansea City moved outside the bottom three after a 2-1 win over Southampton.
The Swans took the lead with six minutes left of the first half as Andy Mawson struck the opener. The Saints drew level with 56 minutes on the clock as Shane Long equalised but Swansea were not to be denied the win as Gylfi Sigurdsson sealed victory with a 71st minute effort.
The Blues opened the scoring in style as David Luiz clipped in a free-kick that swept past the helpless Simon Mignolet in the Reds goal on 24 minutes. Liverpool levelled with a clever effort from Georginio Wijnaldum but could have gone behind when Chelsea were awarded a penalty. Diego Costa stepped up but saw his shot saved as Mignolet went from zero to hero.
Manchester City kept up their top four hopes with a comfortable 4-0 routing of West Ham United.
The Hammers fell behind on 17 minutes as Gabriel Jesus opened his account for the club with David Silva doubling the lead four minutes later. Kevin De Bruyne made it 3-0 six minutes before half-time with the gloss on the win coming on 67 minutes with a penalty from Yaya Touré.
The final game of midweek saw Stoke City and Everton draw 1-1. The Potters took the lead inside seven minutes as Peter Crouch scored his 100th league goal and capped it off with a 'robotic' celebration. Everton levelled five minutes before half-time as Ryan Shawcross hit into his own net.