Killie midfielder Jamie Hamill had a composed debut for a 20-year-old but recalled Colin Nish rarely looked like following his injury-time winner at Motherwell.
Both sides played five in midfield, and that was where play was concentrated in the opening half.
Christophe Berra headed the first effort on target from Bruno Aguiar's 18th-minute corner but Peter Leven comfortably cleared at the far post.
Andrius Velicka fired well wide from a difficult angle after Kestutis Ivaskevicius charged down Frazer Wright's clearance.
Killie only threatened at set-pieces in the first period and Simon Ford twice met Leven crosses but could not head on target. Kingston looked the brightest Hearts player and he showed his frustration at the lack of options as he kept possession well before being forced deeper and deeper.
The Ghanian took matters into his own hands by regularly trying his luck from 25 yards.
He came closest just before the interval, however Graeme Smith comfortably watched his powerful strike fly two yards past the post.
Killie defender Ryan O'Leary replaced Ford at the interval and he was called into action when Hearts threatened with more Aguiar corners, but the only end product was Kingston's misdirected header.
The home side produced some better football moments later but Velicka's diving header was off target following an Ivaskevicius cross.
Steven Naismith fired Nish's low centre back across goal at the other end but the ball drifted out.
Velicka tumbled theatrically in the box but there seemed little contact from Wright and Mike Ritchie waved play on. Hearts' top scorer looked isolated and fans were left baffled when he was taken off for fit-again winger Neil McCann.
Ivaskevicius - without a goal for the club - moved inside from the right wing. Aguiar moved further forward and his dangerous cross just evaded McCann before Julien Brellier threw himself at the ball in vain at the far post.
Leven had a good chance when a set-piece fell to him just inside the box but his shot bounced wide. Head coach Anatoly Korobochka introduced a strike partner for Ivaskevicius when Pospisil replaced Aguiar.
Kingston cleared off the line from O'Leary after Gary Wales had returned Leven's cleared free-kick.
The unmarked Pospisil opened the scoring in the 78th minute when he headed Kingston's inswinging free-kick down and into the net from 10 yards.
O'Leary cleared well from Kingston after a good break from Pospisil as Killie pushed men forward, and the midfielder's clever chip was not far away moments later.
Killie could not mount any concerted pressure but Hearts desperately cleared when a corner almost fell for Naismith in the dying minutes.
A late tackle from Wales on Berra sparked the injury-time melee which saw Goncalves sent off for sprinting 40 yards to remonstrate with the ex-Hearts man.
