Ebbsfleet United were condemned to relegation despite winning a dramatic seven-goal thriller at The Lamb.
Fleet substitute Scott Ginty came off the bench to score twice in four minutes and give his side hope.
But results elsewhere conspired to send Liam Daish's side down to Blue Square South by just a point.
Iyseden Christie, Michael Wylde and Bradley Pritchard netted for the Lambs, Magno Vieira and Ricky Shakes scoring the other goals for Fleet.
After Christie fired the Lambs in front on 11 minutes, it took just 90 seconds for Fleet to level when Magno Vieira headed home Michael West's corner.
Ricky Shakes then fired the visitors in front seven minutes before the break, only for Michael Wylde to level for Tamworth with another header from Neil Mackenzie's corner.
Bradley Pritchard then put Tamworth back in front when he fired home from edge of the box into the top left corner.
Four minutes later Ginty came off the bench and he fired Fleet level again with a shot into the bottom left corner 15 minutes after coming one.
And, although he scored again four minutes later, this time finding the top corner from the edge of the box, it was not enough.
Victories for both Fleet's two main rivals Eastbourne Borough and Gateshead sentenced the Kent side to the drop.
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