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Dave Walder kicked three out of three to secure the win, but huge credit must go to the pack, who were secure in the set piece and cut out the petty infringements that have cost Wasps dearly in the past month.
Joe Worsley had to withdraw minutes before kick off, but the Wasps pack did not seem disrupted and a much improved performance from them, coupled with a typically organised defence, restricted Newcastle to just one Rob Miller penalty.
Cardiff's bonus point win at Scarlets yesterday made this match academic for both sides with no chance of the semi-finals, but Wasps were desperate to draw a line under a run of four defeats in their last five games and half-way through are on course.
Wasps escaped an early set back when Newcastle full back Alex Tait pierced the line and ran through under the posts, only to be called back for crossing with just two minutes on the clock.
That attack stemmed from a penalty against Wasps and they conceded two more in the next four minutes as Newcastle got the verdict at the breakdown.
All were well out of range of the posts though, and Wasps slowly began to ease into it with the scrum providing a good platform for their backs, who moved the ball swiftly through the hands after eight minutes to reach the Falcons' 22 for the first time in the match.
Wasps lost the ball in contact that time and when they tried again on the opposite flank David Lemi was swallowed up by two pink and black hooped shirts.
Newcastle came back at them though, and a series of forward drives weakened Wasps' resistance on their own 22 and when referee Andrew Small awarded the home team a penalty it might have been something of a let off.
Rob Miller did the honours from in front of the posts to make it 3-0 after 15 minutes.
Wasps were still looking threatening in open play though. Dave Walder's chip and chase on the half way line nearly created an opening and when the ball broke loose Ben Jacobs would have sent Lemi chasing had his attempted kick forward not struck a Newcastle chest.
They went even closer after 21 minutes after securing good line-out in Newcastle's half and using Zak Taulafo as a battering ram in midfield. Wasps recycled quickly and for a split second had an overlap on the right, but Lee Smith's chip down the line had too much weight.
With 28 minutes gone they had a chance to draw level when a successful kick chase won them a penalty 45m out, but Walder backed his forwards by kicking for the corner and was rewarded with a clean line-out and disciplined forwards drive.
Again it looked like they had worked an overlap on the right, but Newcastle's covering defence got over in time.Wasps weren't finished though. Another solid scrum gave the Wasps backs a chance, but a promising attack fizzled out into nothing when Jacobs' inside pass went to ground.
The half ended strongly for the visitors though, stealing a Newcastle line-out three minutes from the break and winning a penalty which Walder again kicked to the corner.
The forwards did their job and this time, when Newcastle infringed in front of the posts Walder took the opportunity to make it 3-3 with the last kick of the half.
The Wasps pack got another confidence boost at the start of the second half, when Newcastle tried to drive over in the corner but broke apart against the visitors and eventually conceded a penalty.
It set the tempo for the second period, and within minutes Wasps were probing deep in opposition territory. Steve Kefu nearly picked his way over for the first try, and a huge effort from the forwards got them to within a yard of the line.
A misplaced pass allowed Newcastle to escape that time though, and Charlie Amesbury hacked the ball behind Lee Smith.Walder anticipated the danger though, and after 67 minutes he came to Wasps' rescue again when Newcastle had two men standing open on the wing. Smith had been drawn infield but had not stopped the attack, and it would have been a walk-in try had Walder's out-stretched arm not blocked the pass.
In between the Wasps man had converted his second penalty to make it 6-3, but it was beginning to look a precarious lead.
By 72 minutes Wasps had used all their replacements and the cohesion and control had gone from their play. Newcastle were coming at them in waves and for Wasps it was just a case of whether they could survive till the end.
A relieving kick from Walder bought them some time but Wasps handed possession straight back at the line-out and for a moment the Falcons looked like cutting through. But the home side picked a good afternoon to have a dip in precision and time and again knock-ons and fumbles let Wasps off.
A knock on in midfield handed Wasps possession with four minutes to go, and Walder saw it out with two surgical kicks.The first into the corner pinned Newcastle back and when they infringed again, his third penalty of the afternoon wrapped up the victory.