The Wales flanker, 35, is now a coach at Rodney Parade — but marked his first run-out this season with a stuning second-half show.
Newcastle were leading 14-13 when Charvis went on as a 52nd-minute sub and set up a try for Tom Isaacs just seven minutes later.
Falcons had come from 10-0 down, a penalty try and Ollie Phillips’ score wiping out a try by Marc Stcherbina.
But they had no answer to the class of Charvis and fly-half Jason Tovey’s try took his personal tally to 15 points.
Newcastle boss Steve Bates said: “Charvis stole the ball from a ruck five minutes after he came on but he’s one of those players with experience who will do that.”