On a wet and muddy afternoon at the Rec, the scrum-half’s touchdown followed tries by Ollie Lawrence and Ted Hill, with Orlando Bailey converting all three and adding a 79th-minute penalty.
Bath’s fourth league victory of the season means they complete the double over Newcastle, whose only try came from hooker Jamie Blamire.
After hours of incessant rain, neither side looked far beyond the boot and maul as their favoured tactics until the 13th minute when Bailey dinked the ball over the defence.
A slithering Sam Stuart failed to gather the ball, then watched helplessly as Lawrence surfed in to score under the posts. Bailey added the conversion.
Bath had built their early pressure on the visitors’ indiscipline, but now it was their turn to give away needless penalties in their own 22.
Brett Connon first cashed in after 17 minutes with a straightforward kick and when referee Jack Makepeace gave a dubious knock-on decision against Matt Gallagher, they turned the screw.
Persistent infringements led to a yellow card for Niall Annett and Bath’s seven-man maul defence eventually cracked, as his opposite number Blamire finished off a catch-and-drive, with the try being converted by Connon.
A two-minute session of kick-tennis between the sides drew ironic cheers from the sell-out crowd of 14,509, but the Falcons were looking the more assured outfit.
Even more so when flanker Gary Graham picked a perfect line off a ruck on the Bath 22, only for Hill and Dave Attwood to wrap him up as he crossed the try-line, somehow preventing the touchdown.
Bath were on the back foot for the rest of the half and were indebted to No 8 Josh Bayliss for a turnover at a ruck just short of the try-line.
A second Connon penalty five minutes into the second half put the Falcons 13-7 ahead. But a couple of minutes later, a moment of magic by Lawrence, stepping through the mud, had Newcastle under such pressure that full-back Elliott Obatoyinbo was sin-binned for killing a ruck.
Bath worked the ball left and then to the posts where Hill emerged with a big, muddied smile after touching down, Bailey adding the conversion.
The home supporters were celebrating again 10 minutes later after the TMO confirmed a try by Spencer under a pile of bodies as he celebrated his contract extension in style.
Bailey added the conversion for a 21-13 lead but Connon pulled three points back with his third penalty on the hour.
In a nervy finish, Obatoyinbo let a ball slip through his legs into the in-goal area and only just beat Lawrence to the touchdown.
Bath were content to take control up front, however, and Bailey slotted a 40-metre penalty to clinch victory, while Connon missed an effort at the other end that would have yielded a losing bonus point.