Both sides hit the woodwork in the first half as Willian struck the post with a low shot and Santiago Vergini saw an effort bounce off the bar.
Sunderland continued to frustrate the Premier League leaders after the break and held firm to record their third draw in a row.
The stalemate sees Chelsea extend their advantage at the top to seven points while Sunderland move up to 13th.
The Black Cats were fully deserving of their point too after an impressive defensive display at the Stadium of Light.
While they invited pressure by sitting deep in their own box at times, they always made life difficult for Chelsea and presented them with very few clear chances on goal.
The only time they were nearly caught out in the first half was when Chelsea broke swiftly from a free-kick and Willian struck a low shot against the post from just outside the box.
Wilian was involved in another decent chance on the half-hour mark after linking up with Branislav Ivanovic on the right. The defender continued his run into the box but saw his effort deflected over the bar by Costel Pantilimon.
That, though, was to be Chelsea’s best opening of the half as Sunderland continued to make it difficult for the visitors and started to grow in belief and confidence themselves.
Just moments after Ivanovic’s shot was saved, the hosts spurned a great chance to take the lead when Lee Cattermole’s cross from the right was deflected into the box and into the path of Vergini, who hooked the ball over Thibaut Courtouis but on to the bar.
The Black Cats continued to hold firm in the second half and perhaps even had the better chances to break the deadlock as Chelsea attacks repeatedly broke down on the edge of the Sunderland box.
Connor Wickham nearly caught Courtouis by surprise with a snap shot before Adam Johnson dragged an effort wide on his wrong foot when he should have at least hit the target from inside the area.
The visitors, who saw Diego Costa pick up a booking that will keep him out of the midweek match against Tottenham Hotspur, were largely restricted to long-range shots, but none really tested Pantilimon.
Jose Mourinho threw on Loic Remy and Didier Drogba in a bid to force a late winner but Sunderland were still able to snuff out all of Chelsea’s attacks and hold on for a well deserved draw.
Sunderland: Pantilimon (6), Vergini (7), O’Shea (7), Brown (6), Reveillere (6), Cattermole (8), Larsson (6), Rodwell (6), Johnson (5), Wickham (6), Fletcher (7).
Used subs: Gomez (6), Altidore (6).
Chelsea: Courtois (6), Azpilicueta (5), Cahill (6), Terry (6), Ivanovic (6), Matic (5), Fabregas (6), Oscar (6), Willian (7), Hazard (6), Costa (5).
Used subs: Schurrle (6), Drogba (6), Remy (6).
Man of the match: Lee Cattermole.
RUUD GULLIT’S VERDICT: “Chelsea have to be disappointed with their own performance, especially tactically. Everybody was inside all game and it was exactly what Sunderland wanted. Chelsea were slow paced, with no width at all and only six attempts on target.”