Crichton looks stunned as his 20m-penalty drifts wide
Worcester 23 (6)
Tries: Lutui 2, Quinnell
Pens: Drahm 2
Newcastle 21 (21)
Tries: Woods 2, Thompson
Cons: Crichton 3
Worcester moved off the bottom of the Premiership for the first time since September after securing a priceless win over fellow strugglers Newcastle.
The Falcons were 21-6 ahead at the break thanks to two tries from Ben Woods and one from Matt Thompson.
But Worcester responded with two tries from Aleki Lutui after the break with Gavin Quinnell scoring in injury time.
Newcastle had a chance to snatch the win in the final moments but Loki Crichton missed a penalty attempt.
Crichton had earlier slotted over three conversions but as his 20m-kick from in front of the posts drifted wide, so Worcester started celebrating.
Worcester are now one point ahead of Northampton, who have two games in hand, with matches against Bristol, London Irish and Saracens left this season.
The home side had started brightly and took the lead after just two minutes through a Shane Drahm penalty.
But Newcastle responded within a minute, Woods running in from 25m, and the flanker scored a second on 16 minutes after taking advantage of some poor tackling.
With the Falcons winning plenty of turnover ball, Newcastle were always dangerous and Thompson claimed a simple try just before the break.
Worcester, after what was presumably a harsh talking to at half-time, got back into the game through Lutui on 51 minutes.
Although they struggled to get past Newcastle's defence with the backs, Worcester had more joy with the pack and after lock Craig Gillies won a line-out near the try-line, Lutui touched down for his second try 16 minutes later.
Drahm narrowly failed to add the extras but Quinnell used his power to charge over in injury time.
And with seconds to go, Crichton missed his penalty to gave Worcester the victory.
Worcester coach John Brain:
"I was halfway down the tunnel when Loki Crichton missed that kick. I didn't see it, but I heard the cheer.
"It was a bizarre game in many ways, and we seemed to be in an irretrievable position at half-time, 21-6 down.
"We defended very poorly in the first half against a very good attacking team, but we kept our discipline in the second period and it was a very good fightback.
"We've done our bit to put pressure on the teams around us.
"We have won three in a row, although I have to say that was our worst performance of the three. In the first half, we just weren't at the races."
Newcastle director of rugby John Fletcher:
"That kick would have gone through the sticks 99 times out of a hundred, but on this occasion it didn't.
"But it wasn't just that in terms of the game in general from our perspective. We stopped playing a little bit in the second half and we became illdisciplined which hurt us.
"We scored three tries, but we lost the game through our poor discipline and by making poor decisions.
"Sport can be a cruel business to be in, and today was a cruel day, but credit to Worcester because they put us under a lot of pressure in the second half."
Worcester: Drahm; Havili, Rasmussen, Tucker, Delport; Windo, Fortey, Taumoepeau, Gillies, Murphy, Hickey, Harding, Horstmann.
Replacements: Morris for Windo (41), Lutui for C Fortey (15), Blaze for Murphy (58), Quinnell for Hickey (74), Feaunati for Tucker (67).
Not Used: Runciman, Collins.
Newcastle: Burke (capt); May, Hoyle, Mayerhofler, Rudd; Crichton, Dickson; McDonnell, Thompson, Ward, Sorenson, Oakes, Parling, Woods, Wilson.
Replacements: Long for Thompson (60), Golding for Ward (41), McCarthy for Parling (69), Shaw for Hoyle (10).
Not Used: Buist, Grindal, Dillon.
Ref: Martin Fox (RFU).