The intensity was never really there from the visitors, who fell behind to Jamaal Lascelles' header in the build-up to half-time.
While the Swans were the better side after the break, Moussa Sissoko and Andros Townsend struck late on to seal the points for Newcastle.
The contrasting recent fortunes of both sides were reflected in their team selections. Newcastle and Rafael Benitez made five changes from their loss at Southampton, which saw Daryl Janmaat, Steven Taylor, Jonjo Shelvey, Ayoze Perez and Stefan Mitrovic drop out. Paul Dummett, Jamaal Lascelles, Cheick Tioté, Jack Colback and Papiss Cissé were their replacements. On the other hand, Francesco Guidolin opted for the same eleven that beat Chelsea 1-0 last time out.
Newcastle, despite a slow start initially, managed to start with some attacking intent. Lukasz Fabianski was required to haul a looping cross from Vurnon Anita away from goal, with Cissé somehow unable to take advantage. The striker, instead of directing the ball at goal, managed to clear the danger.
Newcastle strike first
The only bright moment from a Swansea perspective was a potential breakaway, though Jefferson Montero's run was halted - albeit with a cynical foul - by Chancel Mbemba. Gylfi Sigurdsson took control of a free-kick well within his range moments after, although he slipped and the ball landed nearer to the corner flag than the goal.
Colback and Andros Townsend were next to try their luck for the hosts, once again from distance. They were easily dealt with, in a half that looked destined to end goalless. However, Newcastle had other ideas. Townsend fired a corner in towards the near post and Lascelles was on hand to bundle the ball into the net, much to the joy of the hosts.
Spark lacking for the Swans
Crosses were the order of the day early on in the second period, as both teams tried to force an opening from wide areas. Swansea's attempts were rather below par, though Newcastle could have scored a second. The Townsend to Lascelles combination reared its head once again, though the latter couldn't quite connect this time round.
In spite of the early promise, the game was slowly falling back into the dull, drab first-half showing. Modou Barrow was brought off the bench by Guidolin in a bid to spark life back into the attack and he was quickly followed by Bafetimbi Gomis. Benitez responded with Ayoze Peréz and former Swansea man, Shelvey.
Fresh legs give Swansea added impetus
None of the replacements had an immediate impact, yet there was a chance for Ashley Williams as the half drew on. It didn't come from a corner, as many would expect, as a poor clearing header fell to the Swans' skipper on the edge of the area. Williams took aim and thundered a shot narrowly past the post.
Montero and Gomis would waste further chances, with the former going one-on-one with Karl Darlow before lifting the ball over the goalkeeper and past the post. Gomis' opportunity was much more difficult and he scooped over from 18 yards after good initial control.
Hosts leave it late to secure the three points
All that effort would prove in vain as the final 10 minutes saw Newcastle stretch their lead. First, Moussa Sissoko ended a long goal drought by pouncing on a loose ball from a corner. He collected the scraps and rocketed the ball past the helpless Fabianski to make sure of their win.
The tortured Toon were even able to add a third, which could prove crucial for goal difference. Some stylish play provided Townsend the chance to go through on goal, and he slotted under the oncoming 'keeper to take Newcastle up to 28 points. Swansea are down to 15th, still on 40 points.