The Aviva Premiership relegation battle will go down to the last day after Newcastle lost 14-11 to Bath on Saturday.
The win secured Heineken Cup qualification for Bath, who will now finish in the top six.
A late Luke Fielden try earned Newcastle the losing bonus point that could be enough to keep them in the Premiership.
Leeds now have to take at least two points from their trip to Northampton on the final day of the season and hope that the Falcons come away from their return match with Bath empty-handed.
For all the possession and territory they enjoyed Bath only had a Michael Claassens try and a Butch James penalty to show for their dominance in the first half.
The Bath scrum-half worked his way over in the 26th minute after patient build up play by the forwards to cross the Newcastle line, however a lack of accuracy thereafter prevented the visitors building up a sizeable lead at a breezy Kingston Park.
Newcastle once again had to rely on the boot of Jimmy Gopperth to keep them in touch, the New Zealander landing two penalties on a difficult day for kickers.
But Gopperth's most crucial contribution came five minutes time when he launched a rare Newcastle attack inside the Bath half.
The fly-half broke the opposition line and then passed to Tane Tu'ipulotu to put the centre in the clear. Tu'ipulotu raced 40 metres before putting in a grubber kick that was pounced upon by Fielden just before Nick Abendanon got across to cover.
Gopperth struck the upright with his conversion attempt as the Falcons slipped to a seventh straight league defeat, however they look to have done just enough to be playing top flight rugby next season.
Pens: Gopperth 2
Pens: James 2, Vesty
Newcastle: 15 Alex Tait, 14 Luke Fielden, 13 Rob Vickerman, 12 Tane Tuipulotu, 11 Gcobani Bobo, 10 Jimmy Gopperth, 9 Micky Young, 8 Ally Hogg, 7 Will Welch, 6 Tim Swinson, 5 Andrew van der Heijden, 4 James Hudson (c), 3 Euan Murray, 2 Matt Thompson, 1 Jonny Golding.
Replacements: 16 Rob Vickers, 17 Grant Shiells, 18 Kieran Brookes, 19 Mark Wilson, 20 Alex Gray, 21 Chris Pilgrim, 22 James Fitzpatrick, 23 Jeremy Manning.
Bath: 15 Nick Abendanon, 14 Jacques Boussuge, 13 Matt Carraro, 12 Matt Banahan, 11 Tom Biggs, 10 Sam Vesty, 9 Michael Claassens (c), 8 Simon Taylor, 7 Lewis Moody, 6 Ben Skirving, 5 Danny Grewcock, 4 Ignacio Fernandez Lobbe, 3 David Wilson, 2 Lee Mears, 1 David Flatman.
Replacements: 16 Ross Batty, 17 Nathan Catt, 18 Duncan Bell, 19 Josh Ovens, 20 Guy Mercer, 21 Mark McMillan, 22 Butch James, 23 Nick Scott.
Referee: J P Doyle