Postpublished at 21:32 GMT 5 January 2015
Kris Commons almost makes it three for Celtic as Lee Ashcroft makes a mistake in the Kilmarnock rearguard and the visitors' midfielder slams a shot at goal from 22 yards - Craig Samson makes a good save.
Izaguirre and Scepovic score for Celtic
Celtic move one point behind Aberdeen
Ronny Deila's side have a game in hand
Keir Murray
Kris Commons almost makes it three for Celtic as Lee Ashcroft makes a mistake in the Kilmarnock rearguard and the visitors' midfielder slams a shot at goal from 22 yards - Craig Samson makes a good save.
The score now better reflects the play in this match. Stefan Johansen's corner from the right falls between two Kilmarnock defenders but nicely for Efe Ambrose who nods the ball at goal and Stefan Scepovic is alert to poke the ball home from a yard.
Jamie Hamill takes a sore one as a Kris Commons shot thumps off his ankle, seemingly twisting the ligaments, but the Killie midfielder soldiers on. Manuel Pascali thought he was going to get a sub's appearance there.
Andy in Kilmarnock: "What do folk expect about attendance? Monday night on tele. Why would you go?"
Ivan Hamilton in Dunoon: "Come on Killie, do the Dons a wee turn please."
Stuart: "Kilmarnock people do want a football club. But we want one with a chairman who can run a business properly and a manager that can inspire a team to take on average old firm teams."
Kilmarnock's Jamie Hamill snaps the patience of referee Kevin Clancy and is booked for a clumsy trip on Stefan Scepovic.
Celtic skipper Scott Brown is guilty of dithering and his goalie Craig Gordon is at full stretch to palm a powerful Robbie Murihead drive to safety after he latched on to the loose ball.
BBC Scotland football pundit Craig Paterson
"Kilmarnock are just scrapping themselves into the game. It is certainly not as one-sided as it was in the first half."
What a brilliant defensive header by Mark Connolly! Adam Matthews had cut the ball back for Kris Commons in the Killie box and he spun and smashed a shot that looked certain to hit the net. Connolly, though, was for none of that - he dived and headed the ball away inside his six-yard box.
Andy: "Abysmal attendance.....do Kilmarnock people WANT a team in the top flight? Really poor...can't talk up our football based on this."
Kris Commons squeezes a pass through the home defence and in to the penalty box where Liam Henderson crosses a fraction too heavily for Stefan Scepovic whose momentum takes him into the net as the ball drifts out of play.
Jamie Hamill offers some encouragement to the home supporters with a left-foot drive from 20 yards that clips the heel of a team-mate on its way through a ruck of players but goes out for a goal kick. That was a close shave for Celtic.
Kilmarnock have struggled all evening to control the ball for anything more than 15 seconds at a time. The 5,329 fans inside Rugby Park have been watching a steady stream of dark green jerseys towards the Killie goal.
Virgil van Dijk has surely been watching some old VHS tapes of Alan Hansen in his prime at Anfield. Celtic's Dutch defender strolls out of defence, tip-toeing his way past half-hearted challenges and is deep into enemy territory before Alexei Eremenko dispossesses him. However, Liam Henderson picks up the ball quickly and passes in to the home box but Craig Samson gathers.
Kilmarnock get the second period started.
Kris Commons fires a shot at the Kilmarnock goal, one of several attempts in the first half.
Former Celtic assistant manager Murdo MacLeod tells BBC Radio Scotland listeners that the first 45 minutes at Rugby Park are among Celtic's best of the season so far.
Celtic's Emilio Izaguirre is congratulated on his goal by defender Efe Ambrose.
That was a dominant display by the reigning champions, who will feel they should have more to show than a single goal. Killie's only chance was a header from big Josh Magennis, which was well saved by Craig Gordon. Celtic have had 10 shots on goal and have had 63% of the possession.
They've had a few tussles in the past few minutes, but Kevin Clancy has had enough of their jousting. He flashes a yellow card at Celtic scorer Emilio Izaguirre for bringing down Rory McKenzie in a rather "unfriendly" manner.
Killie goalkeeper Craig Samson throws up a powerful right arm to deny Kris Commons scoring a second for the visitors, who blasted at goal from 10 yards.