That may be easier said than done, however.
Since the turn of the year Allan Johnston's side have recorded just two shut-outs, and both came at home. You have to go back to Boxing Day to find the last time they recorded a clean sheet on the road, a 4-0 hammering of Hearts coming at a time when the prospect of Kilmarnock being troubled by relegation matters seemed very remote indeed.
Now they return to Edinburgh hoping to secure the draw that will ensure top-flight football for a 22nd consecutive season and consign Hibernian instead to fight for their SPFL Premiership survival via the play-offs. A 1-0 win over St Mirren on Wednesday night will give Kilmarnock hope. The result not only brought to an end a run of four consecutive defeats but also demonstrated some much-needed defensive doggedness at a crucial time.
"That's only the second clean sheet we've had in 2014 and now we need another one," said Craig Samson, the Kilmarnock goalkeeper. "We showed the other night we can defend. I think people had been questioning whether we could do that. The other night when we went down to 10 men St Mirren really went for it and we showed that we could defend.
"There will be a big crowd backing Hibs but our fans will be there in numbers too and if we can go there with the same spirit I'm confident that we can do it. We have to realise that the job's not done yet and it's a massive game on Saturday. Hopefully we can go as a team and show a bit of resilience and get ourselves over the line."
Kris Boyd was again the hero for Kilmarnock, his 21st goal of the season enough to help his team to three precious points. There will be an expectation on him to do likewise at Easter Road.
"Big Boydy will just notch a treble in 10 minutes and we'll be all right," joked Samson. "Everybody can see what he does for us and what he brings to our team. He gets the plaudits he deserves, especially this season. I can't help but think that if he was in a team in the top half of the table he'd have scored 30 goals.
"We've put a lot of pressure on Kris over the past few weeks to maybe single-handedly get us over the line. But that's never going to be the case. That's why we need to get a clean sheet or put in last-ditch tackles to help him the way that he's helped us."