The Jambos needed a victory at Rugby Park to retain any hope of ending the season in the top half of the table.
However that coveted spot will now be battled out by Aberdeen and Falkirk at Pittodrie on Monday evening, and Hearts face a dispiriting end to the campaign.
Stephen Frail had transformed the fortunes of Hearts since the turn of the year after they had slipped as low as second bottom at one stage, but could not conjure up a win over Killie.
With time running out, Mehdi Taouil could have snatched the winner with a decent effort but Anthony Basso came to the rescue of Hearts again with an impressive one-handed save.
Killie’s Frazer Wright was sent off late on for a second bookable offence.