Falcons' late rally double sinks Bath
The home side had the perfect start when Vereniki Goneva crossed inside five minutes but 17 unanswered points from Bath - through George Ford and Semesa Rokoduguni tries - had given them the advantage.
And although Rokoduguni added a third try, to take him second on Bath's all-time try scorers list, a late rally from the Falcons saw Wilson and Harris cross and snatch the victory.
The Falcons had their first try of the evening with just three minutes gone as winger Vereniki Goneva picked up from the base of a ruck and strolled through a gap in Bath's defence to dot down.
Flyhalf Joel Hodgson, who had made the initial break in the build-up, added the extras to give the home side a 7-0 lead inside the opening five minutes.
With both defences standing strong throughout the first half, Ford missed two penalties to get Bath back into the game.
And as the half came to a close, Ford went for the corner with a third kickable penalty and with phases racking up, the Falcons were penalised in front of the posts and the Bath flyhalf made the score 7-3.
And it was the England international who turned the game on its head minutes into the second half as he collected the ball and jogged underneath the posts for Bath's first try.
With the conversion successful, Bath had the lead in the match for the first time at 10-7 with 43 minutes gone.
And Rokoduguni extended their lead with an excellent finish on 52 minutes as he went over in the corner after being fed by fellow wing Anthony Watson who had made the initial half break.
Despite the close attention of Goneva, Rokoduguni forced himself over the line and with Ford adding the extras from the touchline, the visitors led 17-7.
Hodgson temporarily stemmed the flow with three points for the Falcons on the hour mark but the visitors' momentum wasn't halted as Rokoduguni had his second try of the evening.
It was the winger's 37th Bath try to move him ahead of Iain Balshaw on the club's all-time list with only Matt Banahan ahead of him.
But with ten minutes to play, the Falcons found their form once more though as Wilson forced himself over from close range after a number of pick and drives from the Newcastle forwards.
And trailing by five points with the minutes ticking by, Harris repeated the trick to bring the hosts level and man-of-the-match Hodgson held his nerve to slot the vital conversion.
The scorers:
For Newcastle Falcons:
Try:Goneva, Wilson, Harris
Cons: Hodgson 3
Pen: Hodgson
For Bath:
Tries:Ford, Rokoduguni 2
Cons: Ford 2
Pen: Ford
Teams:
Newcastle Falcons: 15 Alex Tait, 14 Belisario Agulla, 13 Dominic Waldouck, 12 Juan Pablo Socino, 11 Vereniki Goneva, 10 Joel Hodgson, 9 Sonatane Takulua, 8 Opeti Fonua, 7 Will Welch (captain), 6 Mark Wilson, 5 Evan Olmstead, 4 Calum Green, 3 Jon Welsh, 2 Scott Lawson, 1 Rob Vickers.
Replacements: 16 Ben Sowrey, 17 Ben Harris, 18 Paddy Ryan, 19 Will Witty, 20 Sean Robinson, 21 Michael Young, 22 Craig Willis, 23 Fred Burdon.
Bath: 15 Anthony Watson, 14 Semesa Rokoduguni, 13 Jonathan Joseph, 12 Ben Tapuai, 11 Aled Brew, 10 George Ford (captain), 9 Darren Allinson, 8 Zach Mercer, 7 Francois Louw, 6 Tom Ellis, 5 Luke Charteris, 4 Elliott Stooke, 3 Max Lahiff, 2 Tom Dunn, 1 Nathan Catt.
Replacements: 16 Jack Walker, 17 Beno Obano, 18 Shaun Knight, 19 Matt Garvey, 20 Paul Grant, 21 Chris Cook, 22 Rhys Priestland, 23 Robbie Fruean.
Referee: Greg Garner
Assistant referees: John Meredith, Wayne Falla
TMO: Keith Lewis