In the 10th minute, seconds after Paul Dalglish had missed the first of three great chances for the Ayrshire side by shooting over from 12 yards out, Pedro Moutinho's drilled shot from 25 yards put the visitors ahead.
Killie's Moroccan midfielder Mehdi Taouil levelled in the 24th minute with a deflected shot from the edge of the box and from then on, Kilmarnock dominated.
After several more chances went begging, Di Giacomo, on earlier for the hapless Dalglish, popped up to head Garry Hay's cross past Bairns keeper Robert Olejnik to let the Ayrshire side end an injury-ravaged campaign on a high.
Falkirk can have no complaints although defeat meant they did not match last season's points tally.
Before kick-off both sides formed a guard of honour for referee Alan Freeland to mark his last game before retiring and then there was a minute's applause for former Kilmarnock and Celtic manager Tommy Burns who died on Thursday.
The game took time to warm up but in the ninth minute the home side missed an incredible chance after Danny Invincibile drove in to the Falkirk box and slipped a pass to David Fernandez who stretched to lay the ball on a plate for Dalglish.
The man of many clubs had only Olejnik to beat but panicked, blasting his shot over the bar from around 12 yards out.
A minute later Killie were made to pay for that miss when Moutinho picked up the ball 25 yards from goal, turned and drilled a low shot past the flailing Alan Combe.
It was a galling goal to loose for Jim Jefferies' side but they fought back and moments later Fernandez battled to win the ball from Bairns defender Brian Allison on the left-hand side before setting up Invincibile but his powerful drive from just inside the box flew a yard wide.
The pressure continued. A Dalglish corner from the left caused panic in the Bairns box, the ball bouncing around before Chris Mitchell cleared off the line.
But in the 24th minute the home side deservedly drew level after some determined play by Jamie Fowler down the left.
The midfielder's first cross in to the box was cut out by Mitchell but with his second effort he set up Taouil whose deflected shot from the edge of the box fooled Olejnik, who tried in vain to block the ball with his legs only to see it squirm over the line.
In the 36th minute a wonderful cross from wide on the left by the impressive Fernandez found Dalglish with plenty of space at the back post but his header from eight yards out was weak, unconvincing and off target.
With less than 90 seconds gone in the second period, Kilmarnock almost stole in to the lead following a thrilling 40-yard drive by Fowler.
After intercepting a slack pass by Gerard Aafjes, the midfielder went on a mazy run from the halfway line and carved out a yard of space at the edge of the Falkirk penalty area as the visiting defence parted. However, with the Killie fans willing him to finish the move in style, Fowler slipped his side-footed shot wide of Olejnik's left-hand post.
The home side had grabbed hold of the initiative but in the 55th minute Dalglish was the villain for the third time after Taouil's inch-perfect pass had split wide the Bairns defence.
The Killie striker could have taken a touch but snatched at his angled shot from 12 yards and the ball went high and wide, his last effort before being replaced by Di Giacomo on the hour mark.
Falkirk had introduced veteran playmaker Russell Latapy for Patrick Cregg but it was Killie who came close in the 65th minute when Invincibile latched on to Grant Murray's cross but headed over from close range.
Invincible blasted another effort over the bar before Di Giacomo drove across the six-yard box when a bit of finesse might have provided a better dividend.
The luckless Invincibile then drove almost unmolested in to the Falkirk box only to see Olejnik parry his right-footed shot.
It looked like the home side would have to settle for the point but in the 81st minute they eventually forged ahead when Di Giacomo headed Garry Hay's cross in off the post for a deserved victory.