Kris Boyd's first-half winner against St Mirren ended a four-game losing as the home side at Rugby Park held on for a 1-0 win.
They will now travel to Leith a point ahead of Terry Butcher's side knowing a draw is all they need to avoid the relegation play-offs.
But Johnston will not risk his side's Scottish Premiership status by sitting in hoping to earn a stalemate.
He said: "It's a hard one to approach on Saturday. We know we have to go out there with a similar type of performance, the same sort of tempo we played with tonight, and try to get the three points.
"I think it's hard to just play for a point. We've just got to go for it and try to end the season on a high and get the result we need.
"We know it's going to be like a cup final. The Hibs fans will know how vital it is as well - they will get right behind them and there will be a big crowd. You could see with our fans tonight, who were fantastic, that it makes a huge difference. I'm sure they will be there in their numbers as well."
Kilmarnock responded in determined manner after their 5-0 thrashing away to Hearts last Sunday.
Boyd netted at the second attempt 21 minutes in after St Mirren stopper Chris Dilo did well to block his header from an Alexei Eremenko delivery.
But the goal put a dent in Paisley hopes that the Buddies could clinch seventh place and their highest top-flight finish since 1989.
St Mirren chairman Stewart Gilmour will meet the rest of his directors on Thursday, with manager Danny Lennon's future set to be discussed.
The former Cowdenbeath manager is out of contract, but despite leading the club to the League Cup last year there is frustration with his team's patchy league form.
Asked if he had been informed of the agenda for the board meeting, Lennon said: "You know more than me. It's pleasing in this day and age that a manager can see his contract out. I've got to thank my directors for that.
"I'm my own biggest critic - I've made mistakes at St Mirren but ones I've learned from. I'm a better manager for it today.
"I'm not worried about it at all. My remit was to make sure this club stayed in the top flight of Scottish football and I've done that. I've held up my end of the bargain and also won a national cup. On the whole, we've achieved more than the expectation was."