Fly-half Jimmy Gopperth was successful with all five of his penalty attempts to boot the struggling Tynesiders to victory.
Wasps' Christian Wade scored the game's only try but his side were unable to build on it as a spirited Falcons defence stood firm.
Newcastle got off to a cracking start as Gopperth led a second-minute counter-attack, chipping into the 22 and then landing the penalty when Wasps infringed.
The visitors were quick to respond through winger Tom Varndell, who put in a grubber kick to the corner to cause momentary panic, but the opening try came soon afterwards on the other flank.
There looked to be nothing on when Wade got possession from broken play but the speedy wing side-stepped his opposite number and scooted down the touchline in the sixth minute to cross for a fine effort.
Fly-half Ryan Davis put over the simple conversion but was off target with a long-distance penalty attempt shortly afterwards.
Gopperth then pulled back the Falcons' deficit to just one point with a penalty from wide out but Wasps retained the impetus and had the Newcastle line under threat when Davis found a delightful touch near the flag. The line-out ball bobbled dangerously for the Falcons but eventually full-back Alex Tait was able to clear upfield.
A second Davis penalty attempt fell short of the woodwork as the game meandered towards the interval with little in the way of constructive play until, with two minutes remaining, the Falcons raised their game and were rewarded with another three-pointer from Gopperth.
Skipper James Hudson gathered in at a line-out, and a driving maul was on its way into the 22 when Wasps pulled it down and Gopperth's kick made it 9-7 at the break.
Newcastle made a brighter start to the second period, increasing their lead on 46 minutes.
Varndell was caught in possession attempting to run it from his 22, and a hasty clearance made touch.
The Falcons secured the line-out ball and when Wasps strayed offside, Gopperth stepped up to maintain his 100 per cent kicking record.
When the visitors worked their way upfield as lock forwards Richard Birkett and Ross Filipo combined well to drive into the home 22.
The Falcons infringed and Davis had no difficulty with the short-range penalty but at the other end, Gopperth put over a similar effort to restore the Falcons' five-point advantage.
With time running out and the Falcons scenting a long overdue Premiership victory they grabbed the initiative once more, with Hudson leading the way from a line-out midway in the visitors' half.
They pushed the Wasps back in the tight and then at a scrum, and when the visitors did break out in an extended final play Chris Bell was comprehensively bundled into touch to resounding applause.
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