Heffernan replaced Cillian Sheridan after his fellow Irishman pulled up with a hamstring problem moments before the break and proved the difference in a 2-0 victory at Rugby Park.
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 Hampden 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 with more bad luck than they suffered in the lead-up to the first goal of yesterday's match, 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.
Inverness manager Terry Butcher said: "They could be out for a few weeks. It's just our luck, and the transfer window is closed.
"I must have made about five formations. Nick Ross played about four positions and Aaron Doran played about three.
"I don't think we had any luck. The first goal we concede, you can bemoan luck, but it's just not going our way."
However, Butcher admitted his side had not been creative enough as they failed to score for only the second time this season.
"We had opportunities and the keeper has made some saves again but we have not tested him as much as we normally do," Butcher said.
"He has had a quiet game compared to what he normally has against us. That's because the final ball was poor and we kept hitting the first defender, and we have made some bad decisions in and around the box where we have done a lot better this season."