Newcastle had not won away from home in the Premier League since 2015 and Sunday's disjointed affair seemed destined to end goalless until Lascelles headed in after 76 minutes.
Lascelles powered home a header from Matt Ritchie's corner as the Magpies climbed into the top half of the Premier League table.
Newcastle captain Jamaal Lascelles revealed a pre-match telephone pep talk from Rafael Benitez after the Magpies gave their convalescing manager a timely tonic. He had been in such pain this week that he hadn't been able to travel to training.
Deadline-day signings Renato Sanches and Wilfried Bony are set to make their Swansea debuts at home to Newcastle on Sunday after a busy summer of transfer activity at the Liberty Stadium. I am not satisfied with the way we played.
Swansea may have one more point than Newcastle but Newcastle have a better goal difference and have scored more goals.
"Although the margin of the defeat is small I am more disappointed with our performance".
"Very frustrating. I'm finding it hard to understand why I saw what I saw".
Newcastle supporters going to Sunday's top flight fixture have no available trains home
The Swans, who had a horrid opening to their campaign after two crushing defeats, have bounced back well and are on the run of two successive victories after beating MK Dons in the Capital One Cup and Crystal Palace in the Premier League.
"It was a good response because we were getting a lot of stick, and I think it's been unfair".
"I thought they were better than us and I think we missed an opportunity there today, I really do".
"He has been active in the game and kept in touch with us throughout the game". It's a good team, a great group that's got us promoted.
"It was very frustrating and I'm not quite sure why it turned out like that, " said Swansea head coach Paul Clement.
Newcastle make the long trip to South Wales on Sunday afternoon with Rafa Benitez's men looking to build on their first Premier League victory of the season against West Ham before the worldwide break.
'Good brother' Pakistan has 'done its best' to counter terrorism, says China
It is one reason why China is consistently blocking any United Nations resolution against JeM chief Azhar Masood. He said Pakistan had been victim of terrorism for years, and its sacrificed must be acknowledged.