Leeds moved off the foot of the Aviva Premiership Rugby table after coming out on top in a fraught relegation battle thanks to two late drop goals from fly-half Adrian Jarvis.
Defeat means Newcastle now occupy the basement hot-seat after squandering a winning position when they were 20-7 up. Tries from Micky Young and Jeremy Manning, plus 10 points from Jimmy Gopperth's boot, had given the Falcons that handy advantage.
But Leeds added to Steve Thompson's try with scores from Peter Wackett and Gareth Hardy to take the lead. Gopperth hauled Newcastle back into the ascendancy but Jarvis struck in the dying moments.
Newcastle spurned a kickable penalty in the 10th minute to go for the catch and drive and it looked to have paid off with the ball being taken up the Leeds line, but the Falcons pack spilled the ball and Leeds gratefully cleared.
Two minutes later, there was no such risk taken and Gopperth kicked the penalty for a high tackle on Luke Fielden to make it 3-0 and Newcastle's pulverising rolling maul had Leeds backtracking again in the 16th minute and Young wriggled through for a try which Gopperth converted for 10-0.
Leeds got back in the game in the 22nd minute when a sustained drive ended with England hooker Thompson forcing his way over from close range and Jarvis made it 10-7 with the conversion.
Almost immediately Luke Fielden was over the in the corner for Newcastle but the winger lost the ball as he dived in and Leeds breathed again, but they were under the cosh as Gopperth and Young probed to force a penalty which Gopperth kicked in the 28th minute for 13-7.
Ally Hogg's blasting run through the middle set up Newcastle's second try with Manning finishing off a flowing back move in the corner and Gopperth belting over the conversion in the 32nd minute.
Jarvis missed a chance to pull three points back when his penalty shot clipped the post and went wide but Newcastle handed Leeds a try in first-half stoppage time as they failed to find touch from a penalty. Leeds ran the ball back with interest and Wackett scored, Jarvis' conversion made it 20-14 at the break.
Jarvis cut the lead to just three early in the second half with a penalty when Newcastle dragged down a maul and sustained pressure ended with Hardy driving over for a try in the 51st minute to takes Leeds in front for the first time with Jarvis converting to make it 24-20.
Gopperth's 62nd minute penalty cut the lead to just one point as Newcastle finally got themselves on the front foot and five minutes later he edged the Falcons back in front with a fine penalty from near the touchline. But the Leeds pack crushed Newcastle at two successive scrums and turned over a line-out for Jarvis to drop a goal with six minutes left to put Leeds back in front 27-26.
Then with four minutes left on the clock Gopperth landed another massive penalty, only for Leeds to battle their way back and Jarvis slotted his second drop goal with 90 seconds left on the clock.