The home side started brightly despite an early forced substitution of key midfielder Granit Xhaka due to injury, with Brian Brobbey squandering a 15th minute chance, dragging his shot wide.
Chelsea midfielder Morgan Rogers came close to finding the opener with a close-range header but saw his effort narrowly miss the target in the 25th minute.
The Black Cats continued to probe until Levi Colwill fouled Brobbey in the box to concede a penalty that was calmly converted by Enzo Le Fee nine minutes before half-time.
Manager Xavi Alonso introduced forwarded Willian Estevao after the break as the Blues looked to turnaround the result, but the visitors struggled to create clear opportunities until the 75th minute when substitute forced a save from Robin Roefs.
Willian Isidor saw his effort saved by Mike Penders just two minutes later while Cole Palmer's 85th minute header was also saved before substitute Danny Wellbeck missed the best chance, firing wide from close range as Chelsea succumbed to defeat.
The result sees the West London outfit remain in fifth spot on the table while Sunderland moves off the bottom of the log into 18th spot.