Hearts have only taken one point from their last six games to leave themselves 13 points adrift of Killie, who secured their first Scottish Premiership win of the season against Ross County on Saturday.
That run included a disappointing 2-0 home defeat to St Mirren as Hearts missed the chance to move six points behind the Paisley side.
But Smith takes confidence from previous wins over Hibernian and Aberdeen and is determined to improve on that display at Rugby Park on Saturday.
The 20-year-old, who has made 10 appearances this season, told Hearts TV: "It's a massive game again.
"Obviously it was a massive game against St Mirren but I think that's the only game we didn't play to our potential so hopefully this week we play and come away with the three points as we need them.
"It's a must-win game. They're the closest to us in the league just now. The more points we get closer to them, the more pressure we put on them.
"We have proven we are good enough to win games this season so I don't see why we can't win on Saturday."