To add insult to injury Di Giacomo admitted after the game that he had completely mis-hit his shot and that his strike partner Steven Naismith's run across goal had distracted Falkirk keeper Scott Higgins.
Frankly, it was a victory Kilmarnock scarcely deserved. For long periods Falkirk dominated the game but couldn't convert the chances they made and ended up paying the price.
Falkirk were in charge for most of the first half and took the lead after 44 minutes. Russell Latapy took a short corner, exchanged passes with Liam Craig and cut inside before releasing a sublime shot into the top corner from 18 yards.
But the home defence switched off to allow Kilmarnock a shock leveller before the break. Peter Leven's corner was met powerfully by Gordon Greer and when Higgins parried his header, Gary Wales reacted quickly to slam home the loose ball.
It was a more even contest after the break and looked to be heading for a draw before Killie struck three minutes from time.
Di Giacomo hit a scuffed shot from 20 yards, which Higgins expected Naismith to try and get a touch to. The striker instead dummied the ball and Higgins watched in horror as it bobbled into the corner.