The substitute scored with the last kick of the game to give Allan Johnston’s side a first win in nine.
It looked to be heading for a goalless draw with the visitors denied by a string of fine saves by Craig Samson, while Killie’s best chances fell to Robbie Muirhead.
Killie could have taken an early lead when Alex Neil, Accies’ player-manager, was caught in possession but Rory McKenzie hurried his shot from the edge of the box and Michael McGovern made a comfortable save.
At the other end, Ali Crawford’s goal-bound effort was brilliantly parried by Samson.
And the Accies seized control for the rest of the half with Tony Andreu testing Samson from distance with a low effort before Dougie Imrie tested the keeper from close range.
Samson was kept busy for the rest of the half, keeping out Andreou’s first-time effort while Stephen Hendrie arrowed a shot a fraction wide minutes later after a neat one-two.
The home side’s best chance of the first period fell to Muirhead, who could not get the ball out from under his feet with the goal at his mercy.
The second half followed a similar pattern with both sides spurning the few opportunities they created.
Muirhead’s low shot was parried by Michael McGovern while at the other end Crawford’s effort was saved and from the resulting corner, Michael Devlin’s bullet header was cleared off the line.
Despite Neil sending on striker Jason Scotland for the final stages, they could not break the deadlock.
And Eremenko made them pay by hammering his free-kick into the top corner to steal the points in stoppage time.
The result sees the Accies slip to fourth spot while Killie move up to seventh position.