Paul Di Giacomo came off the bench to give Kilmarnock a last-day victory but could not prevent the Ayrshire side finishing second bottom in the SPL.
Pedro Moutinho put visiting Falkirk ahead with a fine drive from 25 yards.
By that time, Paul Dalglish had already squandered one of several chances that were to fall the veteran striker's way.
Mehdi Taouil's deflected shot pulled Killie level and, after a number of opportunities were passed up, Di Giacomo headed home after the break.
Falkirk had already secured seventh place, while Killie went into the game needing a win to have a chance of avoiding finishing eleventh.
Referee Alan Freeland marked his last game before retiring with a pre-match minute's applause in memory of former Kilmarnock and Celtic manager Tommy Burns.
But the reception was more muted from the home fans for the son of another Celtic legend as the game got underway.
Dalglish was picked out David Fernandez, but the former Norwich striker blasted over from 12 yards with only goalkeeper Robert Olejnik to beat.
And, a minute later, the Bairns made the home side pay for that miss when Moutinho picked up the ball 25 yards from goal, turned and drilled a low shot past flailing goalkeeper Alan Combe.
Fernandez set up Danny Invincibile, but the powerful drive from the forward making his return from illness went just wide of the post.
A Dalglish corner from the left caused panic in the Bairns box, the ball bouncing around before Chris Mitchell cleared off the line.
And the home side eventually drew level after 24 minutes, Jamie Fowler crossing for Taouil, whose deflected shot from the edge of the box fooled Olejnik.
The goalkeeper tried in vain to block the ball with his legs only to see it squirm over the line.
Dalglish again squandered a fine chance, heading weakly off target from eight yards following a wonderful cross from the impressive Fernandez.
Olejnik was forced into a decent save from Grant Murray's 16-yard drive.
Falkirk had a chance to steal the lead just before the break when defender Simon Ford had to retrieve his own mistake by blocking a goalbound shot from Bairns wide-man Carl Finnigan.
Kilmarnock were again the more dangerous after the break, Fowler firing wide after a powerful, 40-yard run.
Taouil set up Dalglish, but the striker again fired high and wide.
Invincibile was next to be wasteful, heading over from three yards from a Murray cross.
The Australian was denied by a fine block from Olejnik after being one-on-one with the goalkeeper.
It looked like Falkirk would escape with a point, but Di Giacomo headed in off the post following a Garry Hay cross with 10 minutes remaining.
Kilmarnock: Combe, Murray, Hay, Lilley, Ford, Invincibile, Dalglish (Di Giacomo 61), Taouil (Johnston 89), Fowler, Fernandez (Cox 88), Hamill.
Subs Not Used: Rascle, Frazer Wright, Gibson, Flannigan.
Goals: Taouil 24, Di Giacomo 81.
Falkirk: Olejnik, Mitchell, Allison, Scobbie, Aafjes, Cregg (Latapy 58), McBride, Riera, Moutinho (Stewert 84), Higdon, Finnigan (Barrett 76).
Subs Not Used: Supple, Bradley, Arfield, Moffat.
Booked: McBride.
Goal: Moutinho 11.
Att: 5,475
Ref: A Freeland
BBC Sport Player Rater man of the match: Falkirk's Gerard Aafjes 8.00 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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