Both sides will have viewed the clash as a prime opportunity to claim maximum points for the first time this term, but a closely fought encounter lacked any genuine quality in the final third as promising positions went to waste at both ends.
Marvin Sordell, replacing the injured Danny Ings in the starting line-up for Burnley, spurned the best opportunity of the game in the fifth minute, while substitute Ashley Barnes saw a deflected effort come back off the crossbar with three minutes remaining.
There was another close call in the first minute of stoppage time as Tom Heaton brilliantly tipped Patrick van Aanholt's thumping drive onto the post.
It was a third consecutive goalless draw for Sean Dyche's men, who have now gone five matches in all competitions without finding the net.
For Sunderland, a fourth draw in five league outings this season means Gus Poyet's side remain at the wrong end of the early Premier League table, a point better off than their opponents.
Burnley did at least climb out of the bottom three with this result, but their lack of potency in front of goal may continue to worry Dyche.
Sordell came in for Ings in the hosts' only change, and the former Bolton Wanderers man ought to have put Burnley ahead when he missed his kick from close range after being teed up by Lukas Jutkiewicz.
Emanuele Giaccherini replacing Ricky Alvarez represented Sunderland's solitary alteration from the 2-2 draw with Tottenham, and the Italy international tested Heaton with a firm shot in the 11th minute.
Burnley's David Jones had the next opening in the 19th minute but the midfielder fired straight at Vito Mannone from just inside the area after exchanging passes with George Boyd.
Santiago Vergini flicked a header narrowly wide and Connor Wickham - appearing at Turf Moor for his third different club this year - shot at Heaton as the visitors established a foothold on proceedings.
Heaton was forced to gather Jack Rodwell's strike from distance at the second attempt after the interval, and only Jason Shackell's last-ditch interception denied the former Manchester City man from converting Giaccherini's cut-back in the 55th minute.
Wickham fired narrowly wide from 20 yards nine minutes later as Sunderland began to make inroads, although Mannone had to be alert to keep out Scott Arfield's low cross at his near post soon afterwards.
Jones played in Jutkiewicz in the 77th minute but the striker, after a slight shirt tug from John O'Shea, shot too close to Mannone, who was able to palm away to safety.
Right at the death, Barnes' strike took a wicked deflection and looped over a stranded Mannone only to bounce off the bar, before Heaton and the woodwork denied Van Aanholt as both sides were forced to settle for a point.
