Five penalties from Barkley and a try from flanker Andy Beattie meant that Bath avenge their only defeat meted out by the Falcons in October.
Having four players in the Twickenham jamboree clearly did not improve the Falcons' chances of completing the double.
More serious, however, was the absence through injury of Jonny Wilkinson.
The man with the kicking duties was Dave Walder, who had a miserable day with the boot landing just two out of six place-kicks.
Bath have targeted their three holiday games – they travel to Saracens and Rotherham over the next fortnight – as must-wins so that when they face Wasps at the Rec on February 7 they have an opportunity to open up a virtually unbridgeable gap at the top of the table.
Conditions at Bath were very much against anything but a kicking game but even that was made incredibly difficult in a squally wind.
Barkley was given his first penalty opportunity after just six minutes when the visitors were penalised for handling in a ruck. The fly-half found the target again from 42 metres in the 13th minute, making light of the unpredictable wind, while Walder missed three kicks in the first 20 minutes, one glancing a post.
Bath had the upper hand in the scrums but aggressive Newcastle tackling kept them at bay and prevented the leaders from establishing a foothold in the 22.
However, Newcastle were still prone to give away penalties in the loose play and Barkley hammered over a third penalty on 24 minutes from all of 45 metres.
Walder had a chance to pull back three points on the stroke of half-time but hooked the kick badly into the hospitality boxes.
He was finally on target two minutes after the restart but Barkley replied almost immediately after South African wing Wylie Human and veteran hooker Jonathan Humphreys combined down the left in one of the few dangerous handling moves.
The second half degenerated into a litany of errors and poorly directed kicks before Bath finally managed to rumble over from a line-out, with Beattie being credited with the touchdown.
Newcastle thought they had earned themselves a losing bonus point when flanker Phil Dowson forced his way over from a tapped penalty for a try converted by Walder but even that consolation was dashed by Barkley's fifth penalty in injury-time.
For Bath: Try: BeattiePens: Barkley 5
For Newcastle Falcons:Try: Dowson Pen: Walder