Lascelles headed home a Matt Ritchie corner after taking advantage of the hosts’ slack zonal marking system.
The Magpies skipper was a hero at both ends, clearing a Tammy Abraham shot off the line minutes before scoring the game’s only goal.
Newcastle, missing Rafa Benitez in the dugout due to surgery, climb to 10th in the Premier League table and Lascelles said: “The boys were excellent today. We knew it would be a tough game.
“Swansea like to play football but we knew we could get at them and had a game plan.
“I was mad at myself for letting Tammy Abraham get in that position (clear through on the keeper). Fortunately, I was able to get back and slide in before he hit it.
“With zonal marking, I am not a fan. To see them set up like that I thought we'd get chances. Matt Ritchie has a great delivery. It was my job to get on the end of it.
“I have got great boys around me and great support. We are very close and it follows through on to the pitch.
“These are the teams we need to beat. They are a good side but we were the better team on the day.
“The Premier League is tough and that is why we need to be on it every week.”
Swansea keeper Lukasz Fabianski defended their zonal marking system but lamented their fatal lapse.
He said: “The most frustrating thing is to concede from a set-piece, especially in a game when we are going to try and win it. We got sloppy and got punished.
“It is obvious and clear to see we mark zonally, making two lines to protect the goal. Apart from being in the right position, you have to be aggressive and block the runs. If you don't, then you get punished.
“I don't mind zonal. We have been very successful on it since the manager took over.”
Swansea boss Paul Clement slammed his players for a poor display.
He said: “Although the margin of the defeat is small I am more disappointed with our performance.
“I am not satisfied with the way we played.
“There was expectation going in to the game but we were second best in combats, duels, first and second balls, tactics, in all aspects. I take responsibility for it.
“It is a performance I am not proud of.”
Swansea are 15th after picking up four points from four games.
