In a game that lacked quality but was always intriguing, chances were few and far between on a difficult surface.
Alan Combe was the busier goalkeeper but neither side did enough to secure the victory.
Combe pulled off a terrific save to prevent Falkirk from taking an 11th-minute lead. Gerard Aafjes threaded the ball through to Carl Finnigan but Combe spread himself brilliantly to beat out the striker's 12-yard shot.
Killie responded and Aafjes made a superb block on Danny Invincibile after a flowing move opened up the home defence.
James Fowler then tried to catch out Robert Olejnik with a shot from distance but the goalkeeper stretched to clutch the ball.
The game had opened up a bit after a tentative opening and Finnigan got in behind the Killie defence again only to be caught marginally offside.
Graham Barrett then had an opportunity from a Tom Scobbie corner, but could get no power on his header and Combe gathered easily.
With the wind at their backs, Falkirk looked the more likely and Scott Arfield lashed a shot high over the top from 25 yards.
Iain Flannigan then caused some concern in the Falkirk rearguard with a viciously swerving free-kick which Jack Ross was glad to divert for a corner.
The Killie midfielder then curled a left-foot shot well wide after a short free-kick from David Fernandez.
Darren Barr had a chance to open the scoring shortly before half-time when he met a Kevin McBride corner, but he could not make clean contact and the ball bounced wide.
Substitute Pedro Moutinho almost brought the opening goal with a 50th-minute shot which Combe saved well at his right-hand post.
Both sides had chances in the latter stages. Finnigan had a free header for Falkirk but sent it straight at Combe.
Craig Bryson then burst into the Falkirk penalty area and had chances to pick out a team-mate, but only succeeded in finding the arms of Olejnik.
Falkirk sent on Russell Lattapy and Arnau Riera in the final 15 minutes in search of the elusive goal but Killie held firm.