With the lead changing hands many times, it was the steady boot of Wasps fly-half Mark van Gisbergen that saw the southerners through at the death.
This was the champions' fourth successive win, and rockets them up the Zurich Premiership table to third place, leaving them behind Bath and Northampton only.
With both sides scoring three tries apiece, it was Van Gisbergen's kicking that made all the difference; as he slotted all six of his kicks at goal – three penalties and three conversions.
By contrast, Newcastle's kicker Dave Walder missed three kicks – two conversion attempts and a penalty shot – which would have given his side their first away victory of the season.
The champions looked to be on their way to a comfortable victory after winger John Rudd scored under the posts in the opening exchanges.
But Walder – who had suffered the ignominy of being side-stepped by fellow England international, hooker Phil Greening, in the build-to Rudd's try – made amends by pulling back three points with a penalty.
Wasps, however, replied immediately from the re-start with a try courtesy of former All Black Craig Dowd.
Not to be out done, Newcastle raised their game and a quick tap penalty by scrum-half Hall Charlton opened up the Wasps defence and allowed the omnipresent Hugh Vyvyan to go over in the corner.
Walder adding a brilliant conversion to the flanker's try, and the England man was then awarded a kick at goal just before half-time that would have cut the first-half deficit to one point. But the kick sailed wide and the teams went to break with Wasps leading 14-10.
Van Gisbergen added another penalty early in the second half, but Newcastle fought back thanks to flanker Warren Britz, who broke off the back of a rolling maul to crash over.
Walder missed the conversion and Wasps soon moved clear again when a careless pass by Newcastle fly-half Phil Godman was intercepted by Shane Roiser. The pacy wing ran half the length of the pitch to touch down, leaving Van Gisbergen another easy kick, which he duly slotted.
But still Newcastle continued to fight, their backs launched a devastating counter-attack after a rare mis-hit touch-finder from van Gisbergen. It was wing Michael Stephenson, who eventually crashed over for the try, having been released by a well-time pass from centre Jamie Noon.
But, after watch two more Van Gisbergen penalties sail between their posts, the visitors were left to rue early missed opportunities.
Walder was on target a little while later and pulled his team to within four points, but it was too little too late for Newcastle.
For London Wasps:Tries: Rudd, Dowd, RoiserCons: Van Gisbergen 3Pens: Van Ginsbergen 3
For Newcastlce Falcons:Tries: Vyvyan, Britz, StephensonCon: WalderPens: Godman, Walder 2