The remarkable result at the Stadium of Light saw the hosts secure seventh place, while Chelsea were blue after an unremarkable 10th-place finish.
With only a win enough to keep their European hopes alive, Sunderland began aggressively and eventually broke through in the 25th minute. After sustained pressure, the ball dropped kindly for Trai Hume, who reacted quickly to stab a first-time volley inside the near post from close range, giving Chelsea gloveman Robert Sanchez little chance.
Chelsea struggled to create clear openings before the break and were punished again in the opening of the second stanza.
Brian Brobbey burst into the area and drilled a dangerous pull-back across goal, only for defender Malo Gusto to inadvertently turn the ball into his own goal under pressure, doubling Sunderland's advantage.
But the visitors continued to fight and responded six minutes later through Cole Palmer. The Englishman ended his 14-game goal drought for club and country in style as her collected possession outside the area before drilling a precise low shot beyond Sunderland goalkeeper Robin Roefs to bring Chelsea back into the contest.
However, Chelsea's momentum disappeared when Wesley Fofana was shown a second yellow card for hauling down Wilson Isidor.
Sunderland remained dangerous on the counter and, despite missing further chances, held firm to complete a famous win and book their place in Europe for next season. Meanwhile, missed out on continental football entirely, leaving expected manager Xabi Alonso with a huge challenge.