Arsenal’s hopes of a top-four Premier League finish are all but over after the lacklustre hosts were held by Brighton at Emirates Stadium.
Similarly, Manchester United will also have to settle for Europa League football next season after being held 1-1 by a Huddersfield side who were relegated in March.
The Gunners are three points behind rivals Tottenham in fourth with one game to play but would need an eight-goal swing as well as results going their way.
Pierre-Emerick Aubameyang put Arsenal in front with a ninth-minute penalty after Alireza Jahanbakhsh was judged to have fouled Nacho Monreal despite appearing to get the ball.
Aside from occasional bursts, Unai Emery’s side were shaky and sloppy for long periods, with Granit Xhaka conceding an absurd foul on Solly March to concede a penalty that Glenn Murray converted on 61 minutes.
Arsenal frantically searched for a winner but Aubameyang volleyed wide from seven yards out and Brighton keeper Mat Ryan made a series of fine saves.
Pascal Gross should have won the game for Brighton late on but skewed his effort out towards the sideline with the goal unmanned after Bernd Leno’s superb save from March.
In a frantic finish, young United substitute Tahith Chong had a shot saved and Paul Pogba hit the bar before David de Gea denied Karlan Grant a winner at the other end.
It draw result means United have now gone five games without a win, their worst sequence since they went eight games without a victory under Louis van Gaal between November and December 2015.
The result also means Ole Gunnar Solskjaer’s side cannot catch either Chelsea or Tottenham and have only a slim chance of finishing above Arsenal in fifth.
Alexis Sanchez is also a major doubt for the final game of the season against Cardiff at Old Trafford, having limped straight down the tunnel after suffering an injury at the start of the second half.
Huddersfield are 11 points adrift at the bottom of the table and finish their season at Southampton next Sunday. United remain sixth and entertain Cardiff.
After a quiet first half, Chelsea scored twice within three minutes early in the second period through headers by Ruben Loftus-Cheek and David Luiz.
Gonzalo Higuain sealed the points with a neat finish from Pedro’s pass for his fifth goal for the club.
The win moves Chelsea one point ahead of Tottenham and five points clear of fifth-placed Arsenal, who host Brighton later on Sunday.