Ronny Deila's side have struggled for consistency since winning their first two games of the season, but the victory at Parkhead moves them up to fourth - three points behind table toppers Hamilton Academical with a game in hand and superior goal difference.
Celtic had won the last five fixtures between the sides, racking up 19 goals in the process and rarely looked troubled by their Ayrshire opponents, who came into the game on the back of three straight wins.
Manuel Pascali's dismissal for hauling down a goalbound Stefan Scepovic in the 34th minute hampered Kilmarnock, and their woes were compounded by John Guidetti lashing the resulting free-kick past the wall and home from 20 yards.
The hosts laid siege to the Kilmarnock goal as they sought to put the game to bed, Guidetti seeing an effort crash back off the post before goalkeeper Conor Brennan impressively kept out his follow-up.
Scepovic had also been spurned by Brennan before wastefully shooting off-target with Guidetti well-placed but the Serb was rewarded for his persistence just after the hour as he converted Mubarak Wakaso's centre to give Celtic a two-goal cushion.
Substitute Leigh Griffiths and Charlie Mulgrew each went close to a third late on, though the hosts were happy to settle for two goals and three points which put them back in the driving seat for a title tilt.
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