Northamptonshire remain fifth in the Division One table and secured their place in the division next year, despite Somerset completing a comprehensive victory in Taunton.
Craig Overton finished with match figures of seven for 74 as Somerset also guaranteed their First Division survival.
The day began with the home side looking to dispel any faint prospect of defeat by batting on for nearly half an hour, despite already being 401 in front.
Abell added only three to his overnight score before being caught behind off Ben Sanderson’s first ball of the morning, while Lammonby had extended his tally by nine when pulling a catch to mid-wicket off the same bowler. George Bartlett contributed a brisk 17 before being pouched at deep mid-wicket off Jack White.
Northamptonshire faced a minimum of 87 overs to bat out for a draw. They had reached 14 when hesitation in the middle saw Emilio Gay run out by a direct him from Overton.
Three balls later he pinned Luke Procter lbw for a duck and it was 15 for three when Davey found extravagant bounce off a length to take Josh Cobb’s glove, wicketkeeper James Rew taking a routine catch.
Without a run added, Young edged Overton to Abell at second slip to put Northamptonshire well behind the game.
Ricardo Vasconcelos helped Rob Keogh add 33 before falling just before lunch, leg-before to an Abell angling down the leg side.
It was 49 for five at lunch and the second ball after the interval saw Keogh unfortunate to be adjudged lbw to Davey.
Tom Taylor looks assured for the second time in the match, unfurling a number of impressive cuts and drives in quick succession though he became the next Northamptonshire batsman to be dismissed lbw.
Kasey Aldridge also found surprising bounce from a wicket now offering assistance to the still new ball, Lizaad Williams caught behind fending at a steeply rising delivery. Aldridge claimed a second victim when Ben Sanderson edged a drive through to Rew and the game ended shortly after 2pm when last man White edged Abell to second slip.