Loan signing Marlon Harewood put away two headers and Peter Lovenkrands grabbed another with his head to make it five successive wins for Chris Hughton's men who remain two points clear of West Brom.
Swansea arrived in fourth place with three away wins but sill eight points adrift of Newcastle, but were never in the frame.
The game was effectively over inside the first half-hour as Newcastle powered their way to a three-goal lead.
The writing was on the wall for the Swans as early as the eighth minute when Harewood got on the end of a Fabricio Coloccini cross to score with a deep header.
Newcastle were in rampant form and took a 2-0 lead after 21 minutes, the assist once again credited to an Argentinian - this time Jonas Gutierrez supplying the ammunition for Lovenkrands to head in his first goal of the campaign.
Shell-shocked Swansea were torn apart again seven minutes later when Lovenkrands turned from scorer to provider to set up Harewood for a close-range header.
Swansea were finally stung into action on the half-hour mark but were foiled by some great defending.
An Andrea Orlandi free-kick was cleared by Kevin Nolan from which a Cedric van der Gun shot was saved by Steve Harper at the expense of a corner.
Orlandi's inswinger was again blocked by Nolan at the expense of another corner and United's top scorer was on hand again to deny Darren Pratley.
Harper, struggling with a back injury, was replaced in goal at the break by Tim Krul who found himself with very little do in this one-sided affair.
The home fans got the chance to take a look at new signing Fabrice Pancrate after 76 minutes, the former Marseille man taking the place of Danny Guthrie.
Nile Ranger, on for Harewood who received a great ovation, continues to look for his first goal, but should have done better with a late header from a Lovenkrands cross.