An otherwise dire SPL game at the Falkirk Stadium was lit up by two brilliant bits of goalkeeping from Olejnik, who kept out Mehdi Taouil's free-kick shortly before half-time and Kevin Kyle's late header.
The shot-shy Bairns forced just one save - and an easy one at that - out of Killie goalkeeper Mark Brown during the 90 minutes at the Falkirk Stadium.
The hosts were able to welcome back a trio of first-team regulars.
In came Thomas Scobbie, Jackie McNamara and Burton O'Brien, all of whom missed Wednesday night's Co-operative Insurance Cup third-round thrashing by Celtic.
Killie were forced into two changes from Tuesday's League Cup defeat by St Mirren, replacing the injured Craig Bryson and suspended Manuel Pascali with Gavin Skelton and Danny Invincibile.
The Bairns went into today's game bottom of the table but knew a first domestic win of the season would see them leapfrog their out-of-form opponents.
Their desperation got the better of them in the third minute as Brian McLean clattered into Jamie Hamill, earning a deserved booking.
Otherwise, it was a scrappy start from two sides strling for form and missing some of their more creative players through injury.
With a quarter of the game gone, Kyle laid the ball off to Invincibile, whose sweet 18-yard half-volley was parried away by Olejnik.
Falkirk immediately charged down the other end but Carl Finnigan scuffed his finish wide.
O'Brien skied a 25-yard free-kick just before the half-hour mark before Invincibile received a lecture from referee Stephen Finnie for his reaction after conceding a free-kick.
With half-time approaching, Danijel Marceta was carded for bringing down Hamill on the edge of the area.
Taouil struck a brilliant free-kick matched by an even better save by Olejnik, who somehow tipped the ball onto the woodwork.
There was still time for Invincibile to be cautioned for felling Scobbie before the break.
Falkirk upped the tempo immediately after the break and Marceta curled a loose ball just past Mark Brown's left-hand post from 25 yards.
Kyle, who had scored four goals in his last two appearances against the Bairns, was starting to win possession in the hosts' box.
But it was in his own area that he made the most telling intervention, clearing Darren Barr's header from O'Brien's corner off the line.
With an hour gone, Falkirk threw on Mark Stewart for Kjartan Finnbogason before Marceta hit a bouncing 30-yarder, easily held by Brown.
Scobbie became the latest player booked for furiously protesting after being adjudged to have fouled Steven Old.
Neither side looked capable of fashioning a late winner as the game entered the final quarter.
Falkirk's second change saw Vitor Lima replace Marceta.
Scobbie had tried to get forward all game but his final ball had let him down until a fine cross was met by Finnigan, who failed to connect properly with a header.
Scobbie came off for Marc Twaddle in the final 10 minutes moments before Frazer Wright came off worse in a full-blooded challenge with Stewart and was briefly forced from the field before returning with a bandaged head.
Finnigan was carded after conceding a free-kick just inside his own half and Kyle almost made him pay, his header from six yards brilliantly turned behind by Olejnik.
Gavin Skelton became the sixth player booked in stoppage-time.