Newcastle's victory lifts them seven points above Leeds at the base of the Premiership table
Newcastle inflicted a demoralising defeat on Leeds in the battle of the Premiership's bottom two at Headingley.
Falcons made the perfect start after seven minutes with Ally Hogg's try before Jimmy Gopperth added two penalties shortly before the break.
Newcastle extended their lead with two more Gopperth kicks to make it 17-0.
Leeds' consistent errors and Falcons' stern defending restricted the hosts to Scott Freer's 65th-minute try before Jeremy Manning sealed the victory.
Leeds enjoyed twice as much possession as their visitors but their poor decision making in attack and consistent loss of possession to turn-overs cost them dearly.
The hosts started well enough but fell behind with Falcons' first attack when a blind-side break from a line-out allowed Luke Fielden to feed Hogg, who charged in from 15 yards.
Gopperth missed the conversion but it was one of few mistakes in a fine performance from the New Zealander.
After Leeds squandered several promising attacks their set-piece scrum buckled and the visitors were awarded the first penalty of the game.
Despite losing his footing, Gopperth converted to give his side a crucial eight-point lead in what was still a tight game.
But, when Michael Stephenson was penalised for crossing by referee Dean Richards shortly before half-time, Newcastle's fly-half was on song with a 37-metre strike to make it 11-0 at the break.
The visitors enjoyed good territory in the opening minutes of the second half and Leeds were twice penalised for infringements at the scrum.
Gopperth converted both penalties to pile the pressure on the home side at 17-0.
Leeds' desperation appeared to grow and the game looked to have taken a crucial turn when Newcastle hooker Matt Thompson was sin-binned for killing the ball.
Falcons reshuffled their pack but Leeds could not find a way through as sustained pressure close to Newcastle's line ended with Mike MacDonald losing the ball to Micky Young as he tried to bustle over.
Replacement hooker Freer did eventually cross for the home side but they had already squandered too much possession and when Manning went over in the final minutes Newcastle's victory was already assured.
Leeds still have eight games remaining, including the return fixture at Kingston Park in April, but their belief in Premiership survival will have taken a blow with this defeat.
Leeds Carnegie head coach Neil Back told BBC Radio Leeds:
"We're obviously massively disappointed - this was the first in a run of three home games against opposition we felt we could get results against.
"We hoped to get the ball rolling tonight but it's not happened - there were too many handling errors, 19 or 20 in total, and in the Premiership you can't make that many and expect to win.
"There's still eight Premiership games, forty points up for grabs - it's a game less now to secure points to stay in the Premiership, but we didn't play to our potential today and we weren't good enough.
"We've made it tougher, but the guys have got belief, we're confident we can get the points we need going forward to stay in the Premiership."
Newcastle head coach Alan Tait said: "I was really pleased in how they greeted the win because we said at the start of the week that no matter what the result today we would go away humble.
"I shouted at them at the end to do so - but I didn't really need to because they were exactly that.
"There is still a lot of work to do. Backy [Neil Back] won't let Leeds give in, and we won't either.
"We've now got to look to build on this result. I have said all along this is a good team and if we get things right we are hard to beat.
"Leeds have come up against a side that are starting to pull their straps up."
Leeds: Thomas, Wackett, Fa'afili, S. Barrow, Stephenson, MacKay, Fury, MacDonald, Nilsen, Swainston, Craig, Wentzel, Myall, Browne, To'oala. Replacements: Jarvis for Thomas (60), Burrell for S. Barrow (60), Mathie for Fury (52), Hardy for MacDonald (64), Freer for Nilsen (64), Denman for Swainston (52), Hohneck for Craig (44), Paul for To'oala (64).
Newcastle: Manning, Fielden, Eves, Fitzpatrick, A. Tait, Gopperth, Young, Golding, Thompson, Brookes, Hudson, van der Heijden, Swinson, Welch, Hogg, Pennycook. Replacements: Catterick for Manning (77), Tu'ipulotu for Fitzpatrick (64), Charlton for Young (72), Shiels for Golding (74), Hall for Brookes (68), Vickers for Swinson (58), Pennycook for Welch (41), M. Wilson for Pennycook (69).
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