Two first-half goals were enough to see Newcastle edge out Burnley at Turf Moor.
The goals came from unlikely sources. An own-goal from Ben Mee put Newcastle ahead while Ciaran Clark doubled their lead on the 23rd-minute.
Burnley managed to get one back through Sam Vokes but Newcastle managed to withstand everything else that was thrown at them, though at times it looked like they might be punished for profligate finishing.
It was Newcastle's first win over Burnley wince 1982, and the first win at Turf Moor since 1975.
A professional performance
Things didn't look quite as cohesive as Newcastle's last performance, the 2-1 win over Bournemouth, but it displayed another facet to Benitez' side: a steeliness to edge out a tough away test.
So agricultural was the play at times it resembled some of Newcastle's games in the second-tier, with the long ball style far from the product that the Premier League wants to sell.
But it was physical and full-blooded with dedication from both sides. There was more than a touch of fortune to the first goal, as Mee's heavy deflection took Federico Fernandez's long-range effort past Joe Hart.
But it was a well-taken ball in from Matt Ritchie and a perfectly flicked-on header from Clark to put Newcastle in a well-deserved comfortable position.
After conceding, there was some pressure to withstand before half-time, but that was the only spell of dominance that Burnley enjoyed, and after the break Newcastle came out with a renewed sense of authority, dominating the ball and the balance of chances.
Ritchie produced one of the misses of the season when he had a free shot outside the post, and Kenedy came inches from scoring when he hit the post-late-on. If there's criticism of Newcastle this evening, it's that they should have made it more comfortable for themselves.
Uninspired Burnley
Truth be told, Burnley were unable to ask many questions of Newcastle's makeshift back three because they didn't look like they had many ideas.
Their goal came from a sublime header from Vokes, although there could have been questions asked of Martin Dubravka's positioning.
The tension built late on as Burnley huffed and puffed to find the equaliser, but they were wasteful and struggled to fashion any good scoring opportunities, despite a number of deadly set-piece situations.
On this evidence, Burnley are in real danger of relegation.
Takeaways
Newcastle can cope without Shelvey and Lascelles
The two figures were totemic for Newcastle as they steered away from relegation last season, and would have been said to be vital if they were to do well this season. But it's been three wins without them now. Fabian Schar and Fernandez were sound investments for the backline, while Ki looks a good addition in midfield. They'll be a welcome return when fit again but will have competition for the starting eleven.
Rondon ineffectual without good service
The Venezuelan put in a strong performance as he scored a brace to beat Bournemouth two weeks ago, but to do that regularly he needs quality deliveries. He's a physical target man who will do well with aerial balls into the box, but with that lacking, he was unable to impose much of an influence on the game.
Man Of The Match
Ciaran Clark's header was well-taken, but he also put in an excellent display on the left of a three-man defence. He was important in keeping Burnley's chances limited and wasn't to blame for the goal conceded. Showed Benitez was right to trust him in a back three, with Paul Dummett and Jamaal Lascelles sidelined.