Newcastle dropped points to a newly promoted team for the second successive match as Swansea rode their luck to claim a third away point this season.
Fabricio Coloccini and Demba Ba were denied by the woodwork in the first half, before Jonas Gutierrez sent a thunderous 20-yard drive inches wide.
Ba then wasted a decent chance with a wild volley from Danny Simpson's cross.
Swansea failed to force home keeper Tim Krul into a single save, although Scott Sinclair fired a shot inches wide.
Coming on the back of losing to newcomers Norwich last Saturday, this result extends Newcastle's run without a win to five games.
It leaves Swansea still searching for a Premier League victory on their travels, but manager Brendan Rodgers's side could easily have returned home without a point after soaking up almost constant pressure.
A sombre atmosphere preceded the action as Newcastle paid their respects to former midfielder Gary Speed, who took his own life at the end of November.
Speed's family were in attendance as Welsh tenor Gwyn Hughes Jones delivered a rousing rendition of Bread of Heaven from the centre circle.
A minute's applause followed as fans in the East Stand held up cards each with the number 11 - the shirt number worn by Speed for the Magpies.
Another tribute followed in the 11th minute as the home supporters rose in tribute to a player who played 285 times for Newcastle, scoring 40 goals.
The Toon Army were on their feet again in the 19th minute when Coloccini hit the outside of the Swansea post as Newcastle's dominance started in earnest.
They had already wasted a number of corners and free-kicks around the Swansea penalty area, but Yohan Cabaye's delivery was perfect this time as fit-again captain Coloccini lost his marker at the far post.
Swansea goalkeeper Michel Vorm could claim to have had Coloccini's header covered, but he was beaten four minutes later when Ba's acrobatic effort hit the opposite post.
Complete control followed for the home side, as Swansea were uncharacteristically poor with any scraps for possession.
Further frustration grew for the home side just before the break, when another acrobatic Ba effort from six yards forced Vorm into an instinctive save.
The charmed life of the Swansea goal continued when a thunderous 20-yard drive from Gutierrez swerved inches wide.
And then Ba missed the clearest opening of all, when he failed to control a far-post volley shortly after the restart.
After playing an hour as an anonymous attacking force, Swansea finally advanced into Newcastle territory, but Wayne Routledge's dangerous low ball across the six-yard box evaded the on-rushing Joe Allen.
It was a brief respite for the visitors as Vorm was called into action again to deny Shola Ameobi as the substitute looked to make an immediate impact.
Swansea grew in belief as the Newcastle dominance began to subside in final 10 minutes.
Sinclair found space for a shot at the far post but dragged the effort wide, ensuring Krul ended the match unbeaten.
There was one final chance for Newcastle in the dying seconds, but their frustration was encapsulated by Ba's wild drive high over the bar.
Newcastle manager Alan Pardew: "I really can't complain too much about my side. We stopped them playing, which was the aim, to put them under pressure and force errors, which we did.
"The first half was our better half, for sure. We got in behind and we created chances, we put balls into the box. But they haven't got eight clean sheets for nothing.
"There is a good spirit in the Swansea team and although they didn't keep possession like they would have liked today, they defended very, very well and the goalie looked strong."
Swansea manager Brendan Rodgers: "It was a fantastic performance from us today. It was always going to be a very difficult game coming here.
"Newcastle have had a terrific start to their season and with over 50,000 passionate Geordies, it's always a difficult place to come.
"But the players showed wonderful resilience today to get our eighth clean sheet in 16 games."