The hosts secured a bonus-point by half-time after scoring four first-half tries and, although Newcastle improved after the break, they were ultimately left grateful to Northampton.
The Saints beat bottom club Leeds Carnegie 31-24 at Franklin's Gardens, condemning Neil Back's men to relegation for the third time in six seasons.
Butch James put the hosts ahead in the seventh minute with a penalty and four minutes later they claimed their first try when former Leicester fly-half Sam Vesty went over.
James converted and forward Ignacio Fernandez Lobbe added a second in the 22nd minute when he powered over for a try which James could not convert.
It was one-way traffic and Newcastle, beaten 14-11 by Bath at Kingston Park last weekend, buckled under the constant wave of home attacks.
They shipped a third try in the 31st minute when Matt Carraro crossed the line and James added the extras.
It got worse for the Falcons on the stroke of half-time when England centre Matt Banahan, who missed last weekend's win on Tyneside as his wife was due to give birth, went over for Bath's fourth try.
James converted to put Bath 29-0 up at the break and in total control.
The game was effectively over for Newcastle at that point and, with Leeds leading 24-15 at Northampton at half-time, relegation loomed.
However, Newcastle hit back with tries from Alex Tait and Luke Fielden but Bath added another try through Jacques Boussuge to cap a fine 42-12 win and finish fifth.
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