It was a pretty even opening but when the visitors did try to be more expansive it left them vulnerable at the other end.
Greg Kiltie's attempted through-ball to Alan Power was cut out and it left the latter out of position. Celtic broke quickly and Edouard saw a snapshot deflected just wide of the near post.
Killie were very much in it though, with Stuart Findlay making a surging run out from the back that was only halted by Jullien on the edge of the Celtic box.
It had been a pretty insipid first half for the hosts and, perhaps after a volley from their manager, they started the second period on the front foot.
Almost immediately Jeremie Frimpong burst forward and teed-up Elyounoussi but the winger's curled effort was straight at Rogers.
The right-back himself called the Killie goalkeeper into action moments later, before Edouard's effort was also saved after he connected with a Taylor cross to the back post.
It was an early blitz from Celtic and Shane Duffy should have done better than heading straight at Rogers when he got on the end of a Turnbull free-kick.
The hosts continued to turn the screw and eventually the pressure told, albeit in slightly fortunate fashion.
Elyounoussi hit a low effort from the edge of the box that appeared to be headed straight for Rogers but, in an attempt to block, Aaron McGowan deflected it past his own goalkeeper.
Alex Dyer reacted by throwing on Youssouf Mulumbu and Chris Burke, while Ryan Christie and Patryk Klimala entered the fray for Celtic.
None had the chance to change the game though as Celtic killed it just moments after the changes.
Turnbull sent in another teasing corner and Duffy was left with too much space to rise and power his header into the corner.
Callum McGregor's missed header at the front post gave Killie the chance to reduce the arrears but Nicke Kabamba could only hit it at Hazard from close range.
Christie looked to be in for a third but was denied by a fantastic saving challenge by Stuart Findlay, while fellow substitute Mikey Johnston fired over on his return to action.
Celtic couldn't add the third goal that their second half play deserved but with back-to-back wins and a first league clean sheet since October Lennon will hope a corner has been turned.
Edouard off it
Of the many questions being posed by Celtic fans this season perhaps the most prominent is "what's eating Eddie?".
The French striker is arguably the best player in the country on his day but this term he's struggled to get into any sort of rhythm.
There are mitigating factors, not least a bout of coronavirus, but once again Edouard didn't look at the races and it was no surprise when he was taken off for Patryk Klimala with just over 20 minutes to play. The Polish strikes does a great job of helping his teammates find space.
Power surge
He's looked off the pace at times this season but Alan Power was back to his best at Celtic Park.
The Irishman was everywhere, snapping into tackles and breaking beyond the Celtic midfield when Killie made their forays forward.
He was unlucky to concede a free-kick to Edouard on the edge of the box for what looked a clean tackle.
His efforts were ultimately in vain as Celtic raised the tempo but if Power can maintain this form it'll be a huge boost for Killie going forward.
Duffy finding his feet
Whisper it, but Shane Duffy looks to finally be finding his feet in a Celtic jersey.
The Irishman was brought to add height and power to the centre of a defence which had struggled against physical strikers.
The first dropped points of the season came at Rugby Park as Nicke Kabamba bulled Jullien but the Killie striker barely had a sniff on Sunday.
Duffy won everything in the air and didn't look troubled on the deck, capping off his performance with the crucial second goal.
Let's just not mention that 40-yard effort in the first half.
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