Celtic went into the game off the back of a keenly-contested 1-1 draw at Rennes in the Europa League on Thursday and they had to do things the hard way once again against Killie, as they fell behind to an early deflected strike from Eamon Brophy.
However, a goal either side of half time from Odsonne Edouard turned the match in Celtic's favour before Ryan Christie added a third just before the hour mark - his 10th goal of the season already.
The Bhoys have now won their opening six league games this season and they remain three points clear of Rangers, who recorded a 4-0 victory over St Johnstone on Sunday.
Lennon was pleased with how his side performed against Killie and he believes he is getting the best out of his players.
"That's was a superb performance," Lennon told the club website. "I felt the score line flattered Kilmarnock at half time.
"I'm getting everything I want form this team. We're working the goalkeeper and we're creating lots of chances. This came off the back of a really good performance on Thursday night and we've cemented our league form with a brilliant display today."
Celtic will now turn their attention to the Scottish League Cup, as they will welcome Championship club Partick Thistle to Parkhead in the quarter-finals of that competition on Wednesday.