Chelsea are guaranteed Uefa Champions League football next season and Tottenham Hotspur are all but secure too barring a set of freak results on the final day of the Premier League campaign on May 12.
Arsenal's failure to beat Brighton and Hove Albion as they drew 1-1 ensured delight for both their London rivals.
Glenn Murray's penalty for Brighton cancelled out an earlier spot-kick from Pierre-Emerick Aubameyang as Arsenal's dismal league form continued.
Chelsea had earlier beaten Watford 3-0 and that put them on 71 points in third. With both Arsenal and Manchester United failing to win (United drew 1-1 at Huddersfield Town) Maurizio Sarri's men cannot be caught by anyone outside the top four.
Tottenham are on 70 points, three ahead of Arsenal. But they have a superior goal difference of +8 and it would take Arsenal winning at Burnley, and Spurs losing to Everton, with a swing of nine goals, for Unai Emery's team to take fourth spot.
Arsenal can still qualify for Champions League football though by winning this season's Europa League.
They are 3-1 up after the first leg of their semi-final with Valencia, with the second leg in Spain on Thursday.
Chelsea are also in the semi-finals, and are 1-1 with Eintracht Frankfurt.