Honduran full-back Emilio Izaguirre scored only his third goal in four and a half years with the club in the first half and Stefan Scepovic netted in the second as the Hoops recorded their seventh consecutive win over Killie.
Celtic began the game strongly and came close to opening the scoring when Stefan Johansen beat the offside trap to get through on the Killie goal only for Mark Connolly to get back with a last-gasp challenge to avert the danger.
Johansen threatened again immediately after when he found space in the box after a neat one-two with Scepovic but Connolly again got back to make a goal-saving intervention with a terrific sliding tackle.
The visitors almost took the lead in style on 16 minutes when Kris Commons cut in from the right and unleashed a fierce, dipping left-footed shot which clattered off the Killie crossbar.
Commons looked certain to score minutes later when he beat Lee Ashcroft in the box with some neat footwork but his right-footed shot flashed just over from eight yards out.
Celtic came close again soon after a sustained passing move from the visitors ended with Liam Henderson squaring the ball to Commons, who sent the ball cannoning off the crossbar for the second time in the game.
Killie’s first chance of the night came just before the half-hour mark when Josh Magennis rose above Efe Ambrose to direct Alexei Eremenko’s in-swinging free kick towards the bottom corner but Craig Gordon got down well to save.
Celtic took a deserved lead on 36 minutes after Johansen found Izaguirre with a clever, chipped through ball which the Honduran lashed past Craig Samson on the half-volley.
Commons came close again just before half-time when Henderson played him in with a clever back-heel but Samson got a strong hand to Commons’ rasping shot.
The home side almost equalised soon after half-time when Jamie Hamill’s low, controlled strike from the edge of the box was nearly diverted into the Celtic net by Robbie Muirhead.
Commons’ frustrations in front of goal continued just before the hour mark when he swivelled in the box before unleashing a fierce left-footed shot which Connolly somehow managed to divert over the bar with a terrific diving header.
Celtic finally doubled their lead on 72 minutes when Ambrose rose above Connolly to knock down Commons’ corner and Scepovic was on hand to poke the ball home from a yard out.
Kilmarnock were unable to muster any meaningful attempts on goal in the closing minutes and were fortunate not to concede a third with Commons and McGregor both going close for Celtic.
The win moves Ronny Deila’s to within a point of first-placed Aberdeen with a game in hand, while Kilmarnock stay in seventh.