Stevenson scored the first treble of his career and set up the Edinburgh club's other two goals to leave their opponents in serious danger of joining them in the Championship next season.
Hearts needed only 11 minutes to open the scoring, with Stevenson smashing a free-kick past Craig Samson, with the aid of a deflection, after Sam Nicholson had been hacked down.
The home side thought they had a penalty seconds later when Callum Paterson was seemingly brought down in the box, but nothing was given.
Kris Boyd had an overhead kick go just over the bar as Killie mounted a rare attack but they soon found themselves 2-0 down, with a 24th-minute clearance falling to Stevenson on the edge of the box which he rifled home with his left foot.
Jamie MacDonald saved at the near post from the lively Boyd and Sammy Clingan's swerving free-kick went narrowly over the bar, but Kilmarnock dropped three goals down seconds before the break.
And it was a memorable goal that completed Stevenson's hat-trick - he started the move with a lovely ball out to Billy King and stormed forward to get himself on the end of the winger's cross.
Stevenson skimmed the post with an effort just after the interval and he continued his dominance of the game by setting up Hearts' fourth on 56, his pass giving King the chance to sprint clear and beat Samson from 12 yards.
Four minutes later it was 5-0 and, yet again, Stevenson was at the heart of things with his right-wing cross being bundled in by rampaging full-back Paterson.
Craig Slater had a couple of chances for Kilmarnock late on, firing wide and having a mis-hit shot saved by MacDonald, but there was not even to be a consolation as Hearts played out the final few minutes for easily their biggest win of the season.
Defeat leaves Kilmarnock in 11th with two games remaining in the season, one point adrift of Ross County and two behind Hibernian and Partick Thistle - the 11th-placed finisher will play the winner of the three Championship playoff teams for a place in the 2014-15 SPFL.