Celtic claimed maximum points at Rugby Park thanks to a Georgios Samaras brace and a fine Shaun Maloney strike.
Maloney made up for an earlier penalty miss with a sweet shot into the top corner from 18 yards on 25 minutes.
Samaras then galloped from inside his own half to slide in a perfect finish before tucking away a late penalty.
Celtic defender Gary Caldwell was sent off for handball in the closing minutes, with Mehdi Taouil knocking in the consolation penalty for Kilmarnock.
The home side made life difficult for Celtic throughout a game played at whirlwind pace but the visitors posed much more menace in the final third of the pitch.
Kilmarnock were first to threaten when Manuel Pascali's header took a slight deflection off a defender a few just wide.
With play congested in midfield and lots of meaty challenges flying in, the early period was rather scrappy, with neither goalkeeper seeing much of the ball.
However, the visitors were gifted a glorious chance to open the scoring when Garry Hay clumsily upended Maloney to conceded a 19th minute penalty.
The Scotland midfielder picked himself up and blazed his spot-kick wide, with Alan Combe diving off in the opposite direction.
Combe was then grateful when Samaras cushioned a volley straight at him from close range.
Maloney did not have too long to dwell on his miss since he atoned for his poor penalty with a wonderful goal.
Jan Vennegoor of Hesselink battled with a posse of Killie defenders at the edge of the penalty box and when the ball broke to Maloney, he curled it first time into the top corner of the net.
Five minutes from the interval Shunsuke Nakamura's first-time pass sent Samaras clear and the Greek striker slid his angled, low drive past Combe but also past the far post.
Kilmarnock forward David Fernandez had a great chance to draw the game level but was denied by a point-blank save from Artur Boruc right on the half-time whistle
Celtic continued to look more potent in the second half and in the 50th minute Combe pulled off a great point-blank save from the head of Vennegoor of Hesselink after Maloney had floated in a tantalising cross, defender Simon Ford completing the clearance by knocking the bouncing ball away from the line.
Soon after, Gordon Strachan's men doubled their lead with a fine solo goal from Samaras.
The former Manchester City striker took a Crosas pass and drove down the right flank, leaving centre-back Frazer Wright trailing in his wake before cutting in to the box and drilling the ball past Combe.
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Aiden McGeady, once again left out of the Celtic starting line-up, replaced Maloney on the hour mark and moments later Samaras beat Combe with a curling shot only to see it clip the far post and away to safety.
McGeady was full of tricks as the home side began to tire and Celtic were finding more gaps in the Killie ranks.
With eight minutes remaining, Celtic were awarded a very soft penalty as Nakamura went down under a challenge from Craig Bryson and Samaras converted the spot-kick.
Caldwell was dismissed after an almighty scramble in the Celtic penalty box. He had used a hand to block the ball on the goal-line and Taouil knocked home the penalty, despite Boruc getting close.
Celtic manager Gordon Strachan: "That's as good as we have started against Kilmarnock here. We controlled the game from the very start.
"There were some good performances. Nakamura keeps getting hit and keeps getting back up.
"Samaras was terrific. People forget he's just a young man because of his size - he feels part of the squad and he's definitely helping us right now."
Kilmarnock manager Jim Jefferies: "Celtic played well in the first half and really got on top of us and when we got the ball we were so sloppy.
"I think because of the way things are going, the players think it will just happen for them.
"The second half was better, I thought they competed but then Samaras comes up with a goal."
Kilmarnock: Combe, Fowler, Wright, Ford, Hay (Hamill 71), Pascali, Bryson, Skelton (Sammon 31), Invincibile, Fernandez (Simmonds 71), Taouil. Subs Not Used: Rascle, Lilley, Flannigan, Cox.
Booked: Fernandez.
Goal: Taouil 89 pen.
Celtic: Boruc, Wilson, McManus, Caldwell, Naylor, Scott Brown, Crosas (Hartley 74), Nakamura, Maloney (McGeady 61), Samaras, Vennegoor of Hesselink (Loovens 90). Subs Not Used: Mark Brown, McDonald, O'Dea, Caddis.
Sent Off: Caldwell (87). Booked: McManus, Maloney.
Goals: Maloney 26, Samaras 56, 82 pen.
Att: 8,111
Ref: M McCurry
BBC Sport Player Rater man of the match: Celtic's Georgios Samaras 8.83 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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