Richardson (left) celebrates with Ferdinand after his goal
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.
Sunderland may have been putting in the work-rate but Chelsea carried the greater threat with their crisp passing and movement, with Michael Essien putting a near post header into the side-netting.
The Black Cats fans were doing all they could to help their players and gradually the home side settled before building up a head of steam.
Grant Leadbitter had Sunderland's first shot in anger as he struck a 22-yard effort wide before Kenwyne Jones just failed to get a crucial headed touch to divert cross past keeper Petr Cech.
Sbragia steps down at Sunderland
The loudest roar of the game then cheered a goal but, rather than one for either of the teams at the Stadium of Light, Sunderland fans were celebrating Aston Villa taking the lead against relegation rivals Newcastle.
The visitors had too much experience to let the sometimes surreal atmosphere affect their play and Chelsea striker Didier Drogba's drive forced Black Cats keeper Marton Fulop into a sprawling save.
Sunderland cheers turned to relief when Florent Malouda struck the crossbar with a sweetly struck strike but Anelka was not to be denied as he found the top corner with an angled drive to claim the Premier League's golden boot award with 19 goals.
But the lead did not last long as Cech - under pressure from Jones - missed an attempted catch from Leadbitter's cross to allow Richardson the chance equalise.
Chelsea kept testing Sunderland's resolve and eventually restored their lead when Kalou controlled and shot from just outside the area.
The home side refused to give in and felt they should have had a penalty when Michael Mancienne appeared to block a cross with an outstretched arm.
Hiddink bows out with a win
Chelsea went up the other end and scored to increase Sunderland's injustice.
Anelka flicked on a long ball, which Malouda ran on to only to have his shot blocked before Cole pounced on the loose ball and scored with a right foot shot.
Jones headed in Andy Reid's cross for a consolation goal for Sunderland, who survived with a total of 36 points.
Chelsea boss Guus Hiddink: "We finished off with a good win and especially with a world class goal from Nicolas Anelka.
"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."
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