Marcos Alonso scored the opening goal in the first half with a header. Eden Hazard increased the lead with a brilliant solitary goal. Cesc Fabregas tripled the lead with a fantastic long range shot.
Olivier Giroud pulled one back for the Gunners at the dying moments as a consolation. The win takes Chelsea to 59 points while Arsenal stay at 47.
In another important match, Liverpool conceded yet another shocking defeat at the hands of rock bottom side Hull City. The Reds are on the verge of getting out of the top 4, if Manchester City win today.
Here are all the matches from game week 24
Chelsea 3-1 Arsenal
Watford 2-1 Burnley
Southampton 1-3 West Ham United
Everton 6-3 Bournemouth
West Brom 1-0 Stoke City
Hull City 2-0 Liverpool
Crystal Palace 0-4 Sunderland
Tottenham Hotspur 1-0 Middlesbrough
Manchester City 2-1 Swansea City
Leicester City 0-3 Manchester United