A Robbie Keane double, taking his tally to 11 goals in 11 games since arriving on loan from Tottenham in January, and a Scott Brown strike took the Hoops back to within 10 points of leaders Rangers having played two games more.
Killie skipper Craig Bryson scored a consolation goal for the Ayrshire men whom were outplayed from first whistle to last.
It was exactly the start to his managerial career that Lennon wanted.
The Irishman, who moved up from reserve team manager to replace Tony Mowbray on Thursday following the Hoops’ 4-0 defeat at St Mirren, received a rapturous reception from the home support on emerging from the tunnel to take his place in the technical area alongside his assistant Johan Mjallby.
But despite the fuss surrounding his appointment, there appeared to be no great increase in the attendance which had dipped in recent months.
The Ayrshire men had not won at Celtic since 1955 and they never looked like ending that run.
Less than a minute after kick-off, Marc-Antoine Fortune missed a sitter when he headed Georgios Samaras’ cross over the bar from six yards out, then failed to connect properly with an Andreas Hinkel cross from a similar distance moments later.
As the home side swarmed around the Killie box, Keane had a shot saved by Cameron Bell, who made a better save from Samaras in the 11th minute when he pushed the Greece international’s drive around the post.
In the 18th minute Killie boss Jimmy Calderwood, in an attempt to stem the tide, replaced Mark Burchill with the more defensive-minded James Fowler. The move failed.
Still Celtic dominated as Kilmarnock defended with increasing desperation.
Fortune headed a Lee Naylor cross past the back post in the 32nd minute but they eventually and deservedly got in front three minutes later through Keane.
The Republic of Ireland international burrowed his way into the Rugby Park box and delicately chipped the ball over Bell for his 10th goal since arriving on loan.
A minute from the interval Aiden McGeady’s shot beat Bell but hit the far post and rolled back into the arms of the Killie keeper.
Calderwood made another change at the break, replacing Chris Maguire with Danny Invincibile but to no great effect.
The tempo of the game had dropped and Killie looked as though they were in damage-limitation mode.
However, in the 61st minute Keane settled the destination of the points when he took a Brown pass, turned inside Frazer Wright and drilled the ball past Bell from 12 yards.
It was a poor goal to concede from the visitors’ point of view but there was worse to come.
Four minutes later Brown made it 3-0 when he turned McGeady’s cross-cum-shot past Bell from eight yards with the Rugby Park defence in tatters.
In the 73rd minute the visitors reduced the deficit in a rather fortuitous fashion when skipper Bryson caught Artur Boruc out with a cross from the right which sailed over his head.
Killie survived a penalty claim moments later when Wright looked to have controlled the ball with his arm and their goal led a charmed life in the following minutes.
As the game petered out, Killie striker Allan Russell cracked the bar with a long-distance drive, seconds before McGeady did the same at the other end.
Referee Dougie McDonald did not escape the wrath of the Celtic fans. The official had controversially sent off Brown in the Old Firm game at Ibrox last month and he was booed off at the end after chants were aimed at him in the closing moments.