Younes Kaboul and Troy Deeney struck early in the match to seal the fate. Alex Iwobi pulled one back for the Gunners in the second half but it was not enough. The defeat takes them down to the third position at the moment.
Georginio Wijnaldum scored the equaliser from a header in the second half. Diego Costa had won a penalty in the latter stages of the match but failed to convert it thereby gifting Liverpool a point.
In other important matches, Sunderland held Tottenham Hotspur to a 0-0 draw and Swansea defeated Southampton 2-1 to spice up the relegation battle.
Here are all the results from Day 1 of game week 23
Played on Wednesday February 1
Arsenal 1-2 Watford
Middlesbrough 1-1 West Bromwich Albion
Swansea 2-1 Southampton
Bournemouth 0-0 Crystal Palace
Sunderland 0-0 Tottenham Hotspur
Burnley 1-0 Leicester City
Liverpool 1-1 Chelsea
Played on Thursday February 2
West Ham 0-4 Manchester City
Stoke City 1-1 Everton
Manchester United 0-0 Hull City