Tries from Horacio Agulla, Leroy Houston and Francois Louw, all converted by George Ford, secured the points in the 24-6 win but it was a far from convincing performance.
Bath won 21-0 at Kingston Park in September but found the Falcons a much tougher proposition this time around.
Phil Godman's two penalties even edged them into a 6-3 lead early in the second half before Bath's power game wrested the initiative away.
With Ford released from the England RBS 6 Nations squad along with Kyle Eastmond and Anthony Watson, Bath were missing only Dave Attwood and Paul James (Wales) on international duty.
Leicester's narrow win at bottom club Worcester on Friday night ensured that Falcons arrived at the Rec still with a 10-point cushion over the bottom club.
Jamie Helleur replaced Adam Powell at centre for the visitors, who also brought in Scott MacLeod at lock for Dom Barrow, who has been ruled out for the rest of the season. Argentinian international Gonzalo Tiesi made his Premiership debut.
Ford had a chance to open the scoring inside two minutes but hooked his penalty wide as a squall blew in from the west.
On 10 minutes, Bath lost both hooker Rob Webber and full-back Nick Abendanon to injury, bringing on Ross Batty and Agulla. Carl Fearns had already dropped out just before kick-off, with Houston stepping up at number eight.
Ford missed a 40-metre shot at goal shortly afterwards but finally put Bath on the scoreboard on 16 minutes, although he needed Matt Banahan's steadying hand in the strong wind.
The conditions could not entirely explain the lack of cohesion in the home ranks but Newcastle missed precious few tackles and were happy to see Ford miss another penalty on 26 minutes.
The fly-half did drop a perfectly weighted kick on to wing Sinoti Sinoti, who spilled the ball into touch, but the Falcons came away from their line again and number eight Mark Wilson surged into Bath territory, winning a penalty at the breakdown. Phil Godman levelled the scores from 35 metres.
Bath resumed their siege tactics at the other end, even forcing prop Oliver Tomaszcyk to concede one penalty too many. Despite the yellow card, Newcastle defended their line without too much difficulty for the remaining five minutes of the half.
And they were still down to 14 men when Godman put his side 6-3 ahead after the break.
That finally spurred Bath into a response and, with Matt Garvey driving effectively, Ford's floated pass found Agulla on the right touchline and the Argentine wing cruised over. The fly-half converted and Bath were back in front at 10-6 with 48 minutes on the clock.
Five minutes later, Ford supplied an inside pass for Houston to score under the posts, leaving the youngster another easy kick.
As Bath's confidence lifted, the visitors found themselves trapped in their own half, desperately defending a series of line-out catch-and-drives.
It came at the cost of 18 penalties in all but they never let their heads drop and Bath were denied a third try until the very last minute when Louw stretched out to score. Ford again added the points.