Heffernan replaced Cillian Sheridan after his fellow Irishman pulled up with a hamstring problem and proved the difference in a 2-0 victory at Rugby Park.
A home tie with Hibs stands between the player and a Hampden semi-final appearance.
The 31-year-old fired home in the 58th minute after Inverness debutant Charlie Taylor's clearing tackle ricocheted off the unfortunate Gary Warren and into Heffernan's path.
And, with the visitors stretched, he flicked home Ross Barbour's strike with five minutes left to put Killie in the quarter-finals.
With memories of last season's Scottish Communities League Cup final win over Celtic still fresh, Heffernan believes they can savour more trophy success.
"Obviously with the success we had last year in the cup, it would be great to get to Hamp-den again," he said. "That's what we want to do, we are taking this cup very seriously.
"That was one of the highlights of my career, getting to the cup final and beating Celtic at Hampden.
"In a cup on a one-off day anyone can beat anyone in the SPL so everyone is in with a chance."
Inverness were dealt more bad luck having lost captain Richie Foran and playmaker Andrew Shinnie in the first half-hour.
Foran suffered a knee injury when Warren and a Kilmarnock defender landed on him following an aerial challenge, and Shinnie pulled up with a hamstring strain.