With one game left Chelsea are third with 71 points, a point clear of Tottenham Hotspur in fourth and four ahead of Arsenal.
Chelsea secured a top-four Premier League finish and qualification for next season's Champions League after a 3-0 home win against Watford on Sunday. Quickfire headers from Ruben Loftus-Cheek and David Luiz early in the second half put them in control and Argentine marksman Gonzalo Higuain added a third in the 75th minute.
However, Chelsea had to wait for Arsenal's 1-1 draw at home to Brighton & Hove Albion long after the final whistle at Stamford Bridge to confirm they would finish in the top four.
The battle for the third and fourth spots behind runaway leaders Liverpool and Manchester City had become a comedy of errors in recent weeks with all the contenders dropping points with reckless abandon.
And it was fifth-placed Arsenal's draw with Brighton that meant Chelsea would finish no lower than fourth -- guaranteeing a return to Europe's elite club competition.
With one game left Chelsea are third with 71 points, a point clear of Tottenham Hotspur in fourth and four ahead of Arsenal.
Arsenal need a miracle
Arsenal will need an extraordinary turnaround on the final day after being held to a 1-1 draw by Brighton and Hove Albion on Sunday.
Needing victory to give themselves a realistic chance of securing a Champions League spot, they led through Pierre-Emerick Aubameyang's early penalty at the Emirates only for Glenn Murray's spot kick to drag Brighton level in a frantic second half.
While a win at Burnley and a loss for Tottenham at home to Everton would see the north London clubs finish level on points, Arsenal are eight worse off in terms of goal difference.
Arsenal have now managed to earn only one point from their last four league games -- a run that has ultimately left them needing to win the Europa League to qualify for next season's Champions League.
Earlier, Manchester United's hopes of a Premier League top-four finish were ended after they were held to a 1-1 draw by bottom side Huddersfield Town at the John Smith's Stadium.
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