The Parkhead side have struggled at times in games following Champions League matches this season and indeed had taken only one point from nine following their previous three Group G matches, including a 2-0 home defeat to the Ayrshire side in October.
However, after qualifying for the last 16 of European football's elite club competition on Wednesday night with a 2-1 home win over Spartak Moscow, the Hoops reasserted themselves on the domestic scene to ultimately leave them three points ahead of Inverness with a game in hand.
Inspirational skipper Scott Brown shot the visitors into the lead in the 27th minute and then set up midfielder Joe Ledley for the second after the break, goals that earned both players £20 in a fun wager with boss Lennon.
Substitute Georgios Samaras, on for Lassad Nouioui, then scored with a header as Celtic strolled the final stages before former Parkhead striker Cillian Sheridan grabbed an injury time consolation.
When asked why the performance was so convincing, Lennon said: "I think it is was down to the fact that we are through (in the Champions League).
"The confidence is there, we are not looking a week or two down the line for the next Champions League game and maybe saving a little bit for that.
"We know the consistency in the league hasn't been totally there but away from home we have been very good, we want to replicate that at home now.
"We have opened up a gap and it's up to the other teams to win their games and keep in touch with us.
"Three points with a game in hand is a good position to be in now."
Lennon had no sooner finished lionising Brown at the post-match press conference than the skipper stormed out of the media room after being asked one question too many about his ongoing hip complaint, which he looked to have recovered from.
However, that rather tetchy moment did not detract from the message Celtic sent out to the rest of Scottish football now that they do not have to worry about playing in Europe again until February.
Killie Boss Kenny Shiels claimed there was a "distinct clarity for Celtic now as to how they are going to approach the next few months".
The often controversial Northern Irishman, moreover, was at his cryptic best when he analysed the disciplinary side of the encounter, which saw Liam Kelly, Gary Harkins and Paul Heffernan booked, along with Celtic's Fraser Forster and Brown.
He said: "Our boys were afraid to tackle almost.
"We have the most booking per fouls in the league. We've got the statistics.
"Some clubs it takes 10 fouls to get a booking and it only takes us three - but having said that one was for dissent."
Asked what he believed the reason was for the statistic, Shiels replied: "What do you think? I don't want to go there but you can see there is a disparity.
"But we take our defeat on the chin and we move on. We have tough games coming up."