Newcastle's Matt Thompson can only watch as Matt Carraro scores Bath's third try at the Recreation Ground
Newcastle avoided possible relegation from the Premiership on points difference despite losing at Bath.
Bath needed a bonus point win to try to pip Northampton to a play-off spot.
They had that in the bag by the break as tries from Sam Vesty, Ignacio Fernandez Lobbe, Matt Carraro and Matt Banahan gave them a 29-0 interval lead.
Alex Tait and Luke Fielden hit back for Newcastle but although Jacques Boussuge scored late on, Saints' win over Leeds saved Falcons and ended Bath's season.
Nevertheless, Newcastle were forced to endure an agonising wait following the final whistle for the result to come through from Franklin's Gardens before they could breath a sigh of relief at their Premiership status being secure.
Bath could have done no more to try and snatch fourth place from Northampton, and at one stage it looked as though they would when Saints trailed bottom club Leeds 24-3.
But ultimately, the curtain came down on both their campaign and lock Danny Grewcock's career as Northampton's comeback resulted in Bath finishing fifth.
I think we will go through it again next season. We know we're up against it every single week
Newcastle head coach Alan Tait
Grewcock, who is now retiring from the game, had taken the Recreation Ground field to a deafening ovation and then helped his side dominate the first half.
Butch James kicked an early penalty from 40 metres before Sam Vesty crossed unopposed for the game's first try.
More good work from Vesty allowed second row Fernandez Lobbe to crash over, and although James missed the conversion he made no mistake after Carraro strolled over from a ruck.
The four-try bonus point came seconds before the break when scrum-half Michael Claassens sent Banahan through to score, James again adding the extras.
Tait raised Falcons spirits with an opportunist effort, with Fielden crossing for a second try after James had slotted his second penalty for the hosts.
But, on a day when Luke Watson and James also made their last appearances for Bath, it was perhaps fitting that the home side had the final say when replacement win Boussuge went over under the posts.
Departing Bath coach Steve Meehan: "I said to the players that it won't be long before they are travelling back along the M4 with the Premiership trophy.
"The club is in a good position to capitalise on a lot of good work done with the youngsters in recent seasons."
On the reception he received from the fans: "It was a lovely moment, really appreciated. It will stay with me and my family. I suppose if you could thank the supporters for that, it was with the rugby that we played. It wasn't expected. It was a surprise."
Newcastle head coach Alan Tait: "I think we will go through it again next season. If I say my goal is to survive in the Premiership they'll say I'm negative.
"But I know where these players are and we need a couple of years to get them there. The best way is to get a couple of quality players to play alongside them.
"We know we're up against it every single week. I have to ask them every week to lift themselves against gigantic teams like Northampton and Leicester, even Bath.
"I just saw tired bodies out there in the first half. Last week it was nerves. This week it was fatigue. I can't fault them for effort but we were put to the sword by a Bath team who themselves have a few injuries.
"I feel for Leeds, I do. We need to look at the relegation issue. What's it all for? It was exciting but what does it achieve?"
Replacements: Boussuge for Banahan (68), Williams for James (68), McMillan for Claassens (68), Catt for Flatman (61), Dixon for Mears (61), Palma-Newport for Lilley (20), Watson for Skirving (52), Mercer for Moody (68).
Newcastle: Manning; Fielden, Tu'ipulotu, Fitzpatrick, A. Tait; Gopperth, Young; Golding, Thompson, Murray, Hudson, van der Heijden, M. Wilson, Gray, Hogg.
Replacements: Eves for Fitzpatrick (70), Bobo for Gopperth (47), Pilgrim for Young (61), Shiels for Golding (55), Vickers for Thompson (47), Brookes for Murray (55), Swinson for van der Heijden (55), Welch for Hogg (47).
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