Gus Poyet's men are yet to register a victory in the English top flight this season, but looked the more likely to score during a first half of few chances at the Stadium of Light.
Swansea struggled to find their rhythm and had to wait until the second period for their first shot on target - Gylfi Sigurdsson comfortably denied by Sunderland goalkeeper Vito Mannone.
Connor Wickham headed over from a presentable position in the 74th minute, while Swansea saw Angel Rangel sent off for a second bookable offence before time was up.
Substitute Steven Fletcher nodded just wide of the left-hand post shortly after the visitors were reduced to 10 men, but the scoreline remained goalless.
Sunderland now have five points from their opening six fixtures, while Swansea have 10 after halting their run of back-to-back league defeats.
Wilfried Bony returned from a one-match suspension but was forced to settle for a place on the Swansea bench, with Bafetimbi Gomis preferred in attack, while Billy Jones made his first league start since joining Sunderland on a free during the close-season.
After a slow start to proceedings, it was the hosts who got the first real sight of goal in the 12th minute, Adam Johnson forcing Lukasz Fabianski into a save at his near post following a flicked header from Wickham – back in the team having missed Tuesday's League Cup defeat to Stoke City.
Nathan Dyer has been in a rich vein of goalscoring form during the early part of the 2014-15 season, but his early efforts on Wearside posed little threat to Sunderland goalkeeper Mannone.
South Korean midfielder Ki Sung-yueng – on loan at Sunderland last term - blasted over in the 20th minute as he looked to mark his return to the Stadium of Light with a goal, but chances proved few and far between for both sides during an underwhelming first half.
However, Santiago Vergini had Fabianski scrambling to make a save 10 minutes before the interval when he got his head to a scuffed Sebastian Larsson ball into the penalty area.
Wayne Routledge had appeals for a penalty turned down five minutes into the second half after going down under the challenge of Vergini, before Sigurdsson registered Swansea's first shot on target from 20 yards, drawing a comfortable save from Mannone.
Aside from a flashpoint between Wickham and Swansea captain Ashley Williams, the match was lacking any real spark, and both managers made changes to try and inject some life into proceedings.
Another penalty claim went unrewarded when Wickham went down as he backed into Federico Fernandez, before the Sunderland frontman failed to get on the end of a low Will Buckley ball across the six-yard box.
Wickham headed narrowly over from an excellent Larsson cross 16 minutes from time, yet a goal continued to evade the home side.
Substitute Bony – whose last league goal came at the Stadium of Light in May – looked unlikely to end his goal drought when he fired high and wide shortly after coming on for Gomis.
Swansea's afternoon took a disappointing turn in the 81st minute when Rangel picked up a second yellow card following a collision with Buckley.
It was a second dismissal in as many league matches for Swansea, after Bony saw red against Southampton last weekend, but Sunderland were unable to capitalise as Fletcher squandered their best opportunity late on.
