Kris Boyd and Adam Frizzell scored the Kilmarnock goals which consigned Hearts to defeat in their final game at BT Murrayfield. The Edinburgh club are due to return to Tynecastle Park in two weeks to face Partick Thistle but must do so following three successive losses.
After reverses against Hibs and Rangers, this was a result they desperately wanted to avoid. Boyd put the visitors ahead in the first half but Hearts emerged strongly after the interval. After hitting the goalframe twice, striker Esmael Gonclaves restored parity 15 minutes from time.
Frizzell, though, produced a clever turn and finish to decide the game on 86 minutes. The travelling fans erupted in joy at the prospect of yet another good away result under their new manager, Steve Clarke.
The match was preceded by a minute's silence in honour of those who gave their lives in war as Remembrance Day nears. Kilmarnock arrived eager to recover from Tuesday's 3-0 defeat by Hibs in what was their fourth match under Clarke.
Hearts, with 18-year-old centre-back Daniel Baur debuting at left-back, rattled the post on five minutes - just as the home support began a minute's applause for the late Stefano Salvatori. As hands clapped around Murrayfield, John Souttar's long ball found Goncalves on the run. His strike was netbound until the Kilmarnock goalkeeper Jamie MacDonald pushed it on to the goalframe.
The visitors played the better football of the opening stages, though. They carved a chance for winger Rory McKenzie on 24 minutes with some crisp passing, and Hearts had goalkeeper Jon McLaughlin to thank for a smart save.
Seven minutes later, Kilmarnock did force a breakthrough. Kirk Broadfoot's textbook long delivery found Boyd in behind the home defence. He controlled the ball and calmly slotted it past McLaughlin.
Hearts were toiling to gain some cohesion in their play and fans in maroon grew increasingly frustrated as the first period wore on. Their second-half play was more up-tempo and, on 62 minutes, Goncalves' first-time shot from a corner ricocheted off Kyle Lafferty before MacDonald collected.
The Northern Ireland forward appealed vehemently for a penalty moments later after a challenge by Broadfoot inside the area. Goncalves was then denied by the metalwork for a second time after an exquisite turn and shot, which left MacDonald beaten.
Eventually, the Portuguese's persistence paid off. Receiving the ball in the inside left channel with 15 minutes remaining, he created space to angle a superb right-footed effort towards the top corner. Much to his and his team's delighted, the ball sailed over MacDonald to nestle in the rigging and level the scoreline.
Hearts now had the impetus to go in search of a winner. They would have got one when substitute Cole Stockton slid a pass to Goncalves in behind the visiting defence, but MacDonald emerged to block. Seconds later, the decisive goal arrived for those from Ayrshire.
Stephen O'Donnell's low cutback from the right flank found substitute Frizzell. He turned with his back to goal and confidently dispatched the ball high into the net. The Kilmarnock fans chanted Clarke's name during the closing stages, but for Hearts there is much to ponder during the forthcoming international break.
Hearts (4-4-2): McLaughlin; M Smith, Souttar, Berra, Baur; Cowie, Randall, Callachan, Moore; Lafferty, Goncalves.
76: Stockton for Lafferty
76: Henderson for Randall
87: Milinkovic for Moore
Unused subs: Hamilton, Nowak, Brandon, Petkov.
Kilmarnock (4-4-1-1): MacDonald; O'Donnell, Broadfoot, Greer, Findlay; McKenzie, Power, Taylor, Burke; Jones; K Boyd.
66: Erwin for Boyd
73: Frizzell for Burke
90: Hawkshaw for McKenzie
Unused subs: Bell, Thomas, S Boyd, Brophy.
Referee: Kevin Clancy.