Sunderland were beaten by Chelsea but avoided relegation only for their manager Ricky Sbragia to resign.
Nicolas Anelka put Chelsea in front with a 22-yard shot but keeper Petr Cech missed a cross and Kieran Richardson lashed in an equaliser.
Salomon Kalou drove in a shot to put Chelsea ahead again before Ashley Cole slotted in the visitors' third.
Kenwyne Jones headed in late on for the Black Cats, who stayed up after rivals Newcastle lost 1-0 at Aston Villa.
The Magpies' result came through after the final whistle and will have provided extra satisfaction for the Stadium of Light faithful as, along with Hull losing to Manchester United, it made sure they stayed in the top-flight.
Sunderland manager Ricky Sbragia's future was as uncertain as the club's Premier League status before the game and, although the Black Cats survived, he stood down after the match.
He achieved his primary goal of keeping the club in the top flight but would have achieved that aim a lot easier if Sunderland had shown the same sort of endeavour, energy and enthusiasm as they did for the most part against Chelsea.
The visitors put out a strong line-up with only Frank Lampard and Alex missing but any thoughts they would be distracted by having one eye on next Saturday's FA Cup final proved ill-founded.
Chelsea boss Guus Hiddink:
"My time here has been amazing. Every minute there was good work. The boys responded to what we wanted.
"I challenged them and they responded very well. They are big names and were very good in their attitude."
Sunderland: Fulop, Bardsley, Davenport, Ferdinand, Collins, Malbranque (Healy 78), Whitehead, Tainio (Reid 65), Leadbitter, Richardson (Murphy 87), Jones.
Subs Not Used: Colgan, Edwards, Cisse, McShane.
Booked: Bardsley.
Goals: Richardson 53, Jones 90.
Chelsea: Cech, Bosingwa, Ivanovic, Terry, Ashley Cole, Essien (Kalou 65), Mikel (Mancienne 78), Belletti (Ballack 27), Malouda, Drogba, Anelka.
Subs Not Used: Hilario, Di Santo, Sinclair, Stoch.
Booked: Ashley Cole.
Goals: Anelka 47, Kalou 74, Ashley Cole 86.
Att: 42,468
Ref: Mark Halsey (Lancashire).
www.bbc.co.uk
