The Dragons started with just three regulars at Rodney Parade while the Falcons rested 12 players who began against Gloucester, prompting criticisms of the tournament's meaningfulness.
Tovey opened the scoring with a sixth-minute penalty, before the Falcons threatened to take control with Wales' traditional bane in Anglo-Welsh clashes, the heavy, rolling maul.
Rory Clegg had the chance to equalise with a simple penalty but the 18-year-old academy product - standing in for injured fly-half Wilkinson - scuffed the kick wide.
I'm a better player than coach, we'll see where it goes from here
Man-of-the-match Colin Charvis
A speculative Tovey chip into the Newcastle 22 looked to have been well dealt with by debut-making wing Williams, but after collecting smoothly he allowed Tovey to knock the ball from his grasp, new captain Stcherbina able to gather for the simplest of tries.
Dragons flanker Jamie Ringer was sin-binned for dangerous clearing out at a ruck, the Falcons taking the chance to apply pressure by punting kickable penalties to touch.
They were rewarded when Dragons debutant Anthony Lott collapsed a scrum that was back-pedalling rapidly towards his line, referee Rob Debney awarding a penalty try.
The visitors conceded a penalty straight from the restart, though, allowing Tovey to stretch the half-time lead to 13-7.
That lasted just three minutes of the second period as the Falcons won turnover ball in their own half and off-loaded quickly to wing Phillips.
He chipped ahead and showed lightning pace to squeeze past Phil Dolman for the touchdown, Clegg's conversion giving his side the lead for the first time.
Charvis, 35, was wheeled on for his first appearance of the season on 51 minutes, to a huge roar from the Rodney Parade crowd.
Interview: Colin Charvis and Paul Turner
The veteran soon delivered, barging into a Newcastle ruck for a trademark steal from his feet before powering forward and off-loading expertly to replacement Isaacs, who had the speed to streak in.
Charvis' work on the floor was infectious as his team-mates won a crucial turnover and swiftly attacked the blind-side, Adam Jones off-loading well in the tackle to free Tovey who cruised to the line.
Newcastle fought back and looked sure to score despite desperate Dragons defence, but Russell Winter lost the ball as he stretched for a certain five-pointer, ensuring the Dragons' first win over the Falcons.
Man-of-the-match Colin Charvis:
"There's still a bit of life in me yet, I enjoyed every minute of it, it was just good to get on the pitch with the guys.
"We were always on the edge of taking control, but it just took that turnover and try to get us into our way of playing and we were fortunate to get another win, we're very happy with it.
"I'm a better player than coach, we'll see where it goes from here."
Newcastle rugby director Steve Bates:
"The three Dragons tries came from our turnovers, but some of our boys have played four games in 12 days.
"Colin Charvis stole the ball from a ruck five minutes after he came on.
"He is one of those players who has a lot of experience who will do something like that."
Dragons: Dolman, Selley, Gomer-Davies, Stcherbina, Wyatt, Tovey, R. Lewis, Gustafson, S. Jones, Lott, Hall, A. Jones, Lydiatt, Ringer, L. Evans. Replacements: Connor for Gomer-Davies (44), Isaacs for Wyatt (22), Black for R. Lewis (17), Murphy for S. Jones (55), Charvis for Lydiatt (51). Not Used: Burns, Brown.
Newcastle: Jones, Phillips, Dillon, Davey, D. Williams, Clegg, Young, Golding, Vickers, Ward, Tomes, Swinson, Beattie, Welch, Winter. Replacements: Visser for Davey (55), Long for Vickers (55), Williamson for Welch (58). Not Used: McDonnell, Perry, Charlton, May.
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