The hosts created the majority of the chances, including a first-minute James Dayton free-kick and further opportunities for Paul Heffernan in each half, plus a close call by Gary Harkins after the break.
Hearts had fewer opportunities but saw Stephen Elliott hit the woodwork at the end of the first half and have a goal disallowed for offside in the 83rd minute.
Hearts manager Paulo Sergio made three changes to the side demolished in European action by Tottenham.
David Templeton and John Sutton dropped to the bench, while Ian Black was serving the second and final match of a suspension; their replacements in the starting line-up were Elliott, David Obua and Scott Robinson.
Rugby Park manager Kenny Shiels made two enforced changes - forward David Silva, who has ligament damage, and defender Zdenek Kroca, who had a virus, were respectively replaced by Dean Shiels and Patrick Ada.
Kilmarnock had the first scoring chance inside the first minute - Paul Heffernan strode up the right wing straight from kick-off and was brought down by Adrian Mrowiec, who was booked after just 35 seconds.
James Dayton fired in the free-kick from outside the right corner of the box but it was easily claimed by visiting goalkeeper Marian Kello; then Heffernan was flagged offside to end a promising run as the hosts controlled the opening minutes.
Scott Robinson had Hearts' first effort after 14 minutes with a speculative effort from outside the box following passing build-up, but it failed to test Cammy Bell, who got down to smother it.
However, the hosts continued to dominate the opening quarter, with Dayton and Heffernan looking especially lively - the latter did well to stay onside and reach the byline on 23 minutes, but his cross was too deep for any of his team-mates to convert.
Hearts finally enjoyed their first spell of pressure in and around the penalty area on the half-hour following Andrew Driver's hard work in trying to breach the home defensive ranks.
Obua won the first of three corners, all of which were cleared by the hosts, while Jamie Hamill tested former team-mate Bell with his free-kick from just outside the left corner of the box which the goalkeeper stretched to tip over the bar.
It was Hearts who came closest to opening the scoring nine minutes from the break, when Elliott hit the crossbar with his header from Driver's cross. Bell was beaten by the effort but Kilmarnock booted away the rebound.
Robinson then sent a shot on the turn, from Hamill's ball from the right, wide of the near post in the final minute of the half.
Kilmarnock made a change as the second half got under way, James Fowler coming into defence in place of Ryan O'Leary, who had needed treatment after a goal-line collision earlier in the game.
The hosts made another bright start with a first-minute corner, but Dayton's delivery from the right was confidently punched away by Kello.
Five minutes later, Heffernan did well to meet Rory McKeown's cross from the left with an effort which again called for a strong save, but the home forward was in any case flagged offside.
Gary Harkins was next to threaten for Kilmarnock but bulleted over from the six-yard line after arriving at pace to meet another McKeown cross.
Newly-introduced Templeton and Marius Zaliukas were booked just four minutes apart for bringing down Dayton during promising runs down the right, the second free-kick being cleared to McKeown who blasted over from outside the box.
Bell saw his first action of the second half after 63 minutes when he made an impressive double save, first from Danny Grainger's free-kick after an Ada foul on Elliott, then again from the rebound off his body followed in by Ryan Stevenson.
Liam Kelly lifted a free-kick over the bar after 73 minutes, and the home fans then protested for a penalty when Dayton appeared to be pushed over by Grainger as they battled for possession just inside the box.
At the other end, Stevenson carved out an opening for Hearts with his cut-back from the byline to substitute Rudi Skacel, but Bell claimed the effort.
Hearts finally put the ball in the net seven minutes from time, but Elliott was offside when he converted after build-up from Stevenson and Skacel.