Newcastle's biggest home crowd of the season saw Craig Willis boot two late penalties against Bath to secure a first Aviva Premiership victory of the season.
The Falcons led for much of the match, were pegged back and then came through thanks to Willis, whose last kick of the match secured a 19-14 win in front of 7,075 spectators at Kingston Park.
Bath opened the scoring with a routine line-out dive after Marcus Watson had no option but to concede the line-out in the corner with Matt Banahan breathing down his neck.
Matt Garvey led the line-out drive and skipper Guy Mercer finished it off for a 5-0 lead in the sixth minute.
Willis, who had missed an early penalty for the Falcons, made sure with his 13th-minute effort after Bath came in at the side.
Willis, Simon Hammersley and George McGuigan had the crowd on their feet with some gutsy running, Willis especially making a long and weaving run through midfield, but he then missed a 17th-minute penalty for offside.
It was Willis with another penetrating run that had Bath on the back foot, and Juan Pablo Socino slotted a rolling kick to the corner. When Bath conceded a free kick, Ally Hogg took it quickly and Rob Vickers forced his way over in the 21st minute, Willis converting for the Falcons to lead 10-5.
In rapidly worsening conditions, both sides were having difficulty hanging on to the ball but Bath cut their deficit to 10-8 with a 28th-minute Rhys Priestland penalty when Falcons number eight Nili Latu went over the ball.
Garvey was caught dragging down the maul and Willis missed another kick at goal he should have made regardless of the conditions.
Newcastle went close to scoring a second try with a massive driving maul and Vickers was at the bottom of it again, but this time the referee and TMO ruled he been brought down just short.
However, the referee brought play back for persistent offside which saw prop Henry Thomas sin-binned and Willis kicked the penalty for 13-8, Newcastle's half-time lead.
Latu overstepped again early in the second half and Priestland kicked a 46th-minute penalty with the wind and rain at his back to make 13-11. The Wales international missed a chance to nudge Bath back into the lead shortly afterwards with a penalty that was just wide, before making it 14-13 with a successful attempt in the 58th minute.
Newcastle were clearly under pressure, both at the scrum and kicking into the wind and rain, and they conceded successive scrum penalties on halfway. Priestland kicked the first one dead but found the corner with the second, only for Bath to make a mess of it and concede a penalty for blocking.
It seemed Newcastle had snatched another try when Scott Lawson threw a long pass out and Watson kicked ahead for Chris Harris to be held up on the line.
It led to a penalty which Willis kicked to put Newcastle back in front at 16-14 with 10 minutes left on the clock and within sight of a rare win.
The victory was made secure when, with 40 seconds on the clock, Bath were caught obstructing as Tom Homer ran it out of defence and Willis kicked the penalty to spark the celebrations.