Newcastle (7) 10 Try: Golding Pen: Clegg Con: Miller
Gloucester (6) 11 Try: Satala Pens: Barkley 2
Satala left it late to win the match for Gloucester
Replacement Apo Satala's winning try four minutes from time sent Gloucester into the EDF Energy Cup semi-finals.
For a long period it appeared Newcastle prop Jon Golding's first-half try would be enough to earn the Falcons victory.
But the visitors, for whom Olly Barkley had landed two penalties, were given a late penalty for crossing and, with time running out, chose to run it.
They worked the ball down the right and flanker Satala crashed over for the decisive score.
Gloucester made the stronger start, with Barkley missing an early penalty, and winger Iain Balshaw tested the home defence when he decided to change to the opposite wing, before spoiling the move with a forward pass to Lesley Vainikolo.
Newcastle did not even cross the halfway line until the 18th minute, when Steve Jones hoofed the ball upfield and Gloucester's Willie Walker put the ball out of play.
From the resulting line-out, they worked the ball over to the right wing before the forwards took play back under the posts.
They kept the pressure on and it paid dividends when Golding drove over for the opening try.
Rob Miller added the conversion but Gloucester replied instantly with two quick penalties from Barkley to cut the gap to just one point.
With half-time looming, Vainikolo was hauled up just short of the line and Walker tried a drop-goal, but Newcastle went in one point ahead.
After the restart, Mike Tindall looked sure to claim Gloucester's first try as he charged 30 metres to the line, only to be thwarted by Tom May's tackle which forced him out of play right by the corner flag.
Having chosen to run one kickable penalty and failed to score from it, Newcastle did not spurn the chance when it came round again, replacement fly-half Rory Clegg's long-range effort making it 10-6.
With time running out for the visitors, Balshaw drove deep into Falcons territory before the move broke down for a crossing offence.
They ran the penalty and the resulting try by Satala secured a semi-final against defending champions the Ospreys, at Coventry's Ricoh Arena, on 28 March.
Newcastle director of rugby Steve Bates:
"I'm bitterly disappointed and really upset that we didn't clinch it earlier.
"A little bit of desperation was creeping in near the end and we gave away a lot of penalties.
"It was pretty even in terms of creating and taking chances."
Gloucester director of rugby Dean Ryan:
"We made hard work of it and Newcastle deserve credit, they worked very hard.
"Both Apo and Dave Lewis made the difference when they came on."
Newcastle: Jones, D. Williams, May, Davey, Rudd, Miller, Charlton, Golding, Vickers, Ward, Swinson, Sorenson, Williamson, B. Wilson, Dowson.
Replacements: Clegg for Miller (55), Young for Charlton (63), Long for Vickers (55), Perry for Swinson (66), Winter for B. Wilson (69).
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