Worcester came from behind for a draw after Newcastle failed to capitalise on the lion's share of possession.
The hosts had opened up a 13-3 lead early on with a converted Phil Dowson try and a pair of Rory Clegg penalties.
But the Warriors slowly fought back, Eoghan Hickey trimming the lead with two penalties before half-time, with Adam Balding harshly sin-binned.
And they grabbed a share of the spoils when Pat Sanderson crossed, and Hickey converted, 11 minutes from full-time.
The match turned on a mistake by young Newcastle fly-half Clegg when he tried to throw the ball into himself close to his own line, slipped and lost control of the ball.
Worcester snaffled it, swept it wide and eventually scored through Sanderson.
Newcastle coach Steve Bates:
"You can't blame Rory. You have to take the rough with the smooth with these young guys who are talented but inexperienced.
"If he'd caught it and banged it 40 metres into touch we'd all be standing here saying he was brilliant.
"I was one of our best performances of the season but I suppose we didn't finish things off as well as can."
Worcester director of rugby Mike Ruddock:
"We were very disciplined and I was very pleased with the character we showed at the end when Newcastle were coming at us.
"To come back from 13-3 down to get a draw is a real plaudit to the players.
"We stayed calm and composed and showed character. Hopefully, we can keep it like that and move up the league."
Newcastle: May; Visser, Noon, Tu'ipulotu, Rudd; Clegg, Young; Golding, Thompson, D Wilson, Swinson, Sorenson, Balding, B Wilson, Dowson.
Replacements: Grindal for Young (59), Hayman for D Wilson (33), Parling for Balding (59).
Not Used: Vickers, Brown, Miller, Jones.
Sin Bin: Balding (33).
Worcester: Latham; Gear, Rasmussen, Tuitupou, Pennell; E Hickey, R Powell; Mullan, Lutui, Horsman, Rawlinson, Gillies, Talei, Sanderson, Horstmann.
Replacements: M Powell for R Powell (61), Bowley for Gillies (56), Tuamoepeau for Horstmann (56).
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