Steve Bruce’s team once again looked toothless in attack and have now managed to score just 24 goals in 28 top-flight games this season.
After a mediocre start to the match, Newcastle went close to taking the lead in the 18th minute when Dwight Gayle got on the end of Javier Manquillo’s cross, only to see his shot blocked.
At the other end, Martin Dubravka did well to tip Jeff Hendrick’s cross-cum-shot over the bar.
Jonjo Shelvey, back in the Newcastle side after an injury lay-off, had a shot blocked before Clarets goalkeeper Nick Pope saved Miguel Almiron’s effort.
Matt Ritchie’s goalbound shot was charged down by Jay Rodriguez as a grim first-half ended goalless.
Shelvey seemed to be the most likely player to break the deadlock but the former Liverpool and Swansea City midfielder lifted a 51st-minute shot over Pope’s goal.
Burnley improved when Chris Wood came off the bench and the New Zealand international looped a header over the crossbar, but clear-cut chances continued to be at a premium as the second half wore on.
Gayle’s acrobatic 65th-minute effort flew narrowly wide and Ritchie’s 25-yard thunderbolt failed to trouble Pope as a poor game drifted towards its conclusion.
Newcastle almost snatched all three points in stoppage time when Shelvey led a rapid counter-attack and played in Ritchie, only for the former Bournemouth midfielder’s shot to be blocked.