An emotional day, following the death of the man who captained the side that won the European Cup in 1967 and later went on to manage the club, did not quite go to plan for over an hour.
Despite being mostly on the back foot Killie arguably had the better chances before the break while Celtic had numerous and mostly inaccurate efforts on goal.
However, Simunovic – wearing the number five so closely associated with McNeill – headed in a Callum McGregor cross with 67 minutes showing on the clock to give the hosts a 1-0 Ladbrokes Premiership win.
With three fixtures remaining, Celtic moved 12 points ahead of second-placed Rangers – and they could secure an eighth successive title as early as Sunday if their Old Firm rivals slip up at home against Aberdeen.
Interim boss Neil Lennon, who along with skipper Scott Brown had laid a wreath at McNeill’s statue outside the stadium before the game, made two changes with midfielder Tom Rogic and winger Scott Sinclair coming in for Olivier Ntcham and Jonny Hayes.
Injury and suspension meant Killie boss Steve Clarke had to field a makeshift central defence of on-loan veteran Alex Bruce and midfielder Gary Dicker.
On-loan midfielder Youssouf Mulumbu was not allowed to play against his parent club while Aaron Tshibola, Conor McAleny and Liam Millar were handed starts.
There was as an appropriate 67-second round of applause in McNeill’s honour before the game and when the action got under way Celtic, wearing black armbands with number five on them, looked most likely to make the breakthrough.
Brown, Emilio Izaguirre, Odsonne Edouard and Rogic all had efforts on goal of varying quality.
However, in the 14th minute there was a Killie penalty claim when Brown challenged defender Stephen O’Donnell inside the box but referee Willie Collum waved play on.
Four minutes later the Ayrshire side had a great chance when former Rangers winger Chris Burke found himself clean through on goal after the break of the ball but Hoops goalkeeper Scott Bain made a crucial block.
Bain then had to make good saves from Millar and McAleny as Killie grew in confidence.
In the 27th minute, Celtic defender Kristoffer Ajer gifted Eamonn Brophy possession but made a fine recovery tackle as the Rugby Park attacker took too long to get his shot away.
It was another let off for the home side but Killie still had plenty of defending to do before reaching half-time goalless.
More attempts on goal by both sides followed early in the second half, most notably when Bain had to stretch to tip Burke’s curling effort from 20 yards over the bar after Hoops defender Mikael Lustig had passed straight to him.
Amid increasing Hoops frustration, Edouard curled a shot wide, Killie keeper Danny Bachmann made a great save from McGregor and O’Donnell stopped Edouard getting on the end of Rogic’s pass.
However, that frustration was replaced with joy when Simunovic leapt to head McGregor’s past the flailing Bachman.
The game stretched further as the visitors threw men forward in search of the equaliser – but perhaps the match was destined to be decided by Celtic’s number five.