After Kris Commons capitalised on a mistake by Killie keeper Craig Samson to give the Hoops the lead in the 19th minute, the Greece forward scored twice within two minutes, the first with a guided volley and the second after a good one-two with Commons.
Kilmarnock midfielder Sammy Clingan, playing his first game of the season after recovering from a knee injury, reduced the deficit with a great free-kick before defender Sean Clohessy made it 3-2 just before the break.
However, Samaras sealed the win in the 87th minute with a header before substitute Amido Balde, on for Teemu Pukki, scored a fifth two minutes later.
Afterwards, the Celtic boss said: "I thought he was world-class today.
"You can talk about the standard of SPFL football or this and that but when you see a player play as well as that, no matter the standard, you can tell that he is a top-class player.
"I thought he was brilliant. Everything about his game was of the highest quality.
"I am delighted he got the goals but even if he hadn't got the goals, I thought his all-round play was magnificent."
Samaras, however, was almost unwilling to accept the praise of Lennon.
And for a player who had just scored his first hat-trick in three years, he cut a very subdued figure in the Rugby Park media room.
The Greece striker said: "It is just goals, just three points.
"It is not a really important thing.
"The important thing is at the end of the season to win the trophy.
"If we don't win the trophy what is the point of scoring a hat-trick against Kilmarnock?"
Kilmarnock boss Allan Johnston is still looking for his first win of the season but was heartened by his side's "spirit" in a match that took place against the background of rancour at Rugby Park.
Kilmarnock chairman Michael Johnston had upset the club's fans by giving Celtic season ticket holders - but not their own supporters - the chance to buy cut-price tickets for the game which was watched by a relatively low crowd of 6,149 fans, most of them in green and white.
Johnston responded to criticism by announcing new incentives for home supporters.
Nevertheless, there was a small protest outside the ground before the game and Johnston accused fans' leaders of attempting to force the club into administration by withholding revenue from ticket sales.
"Their leaders advocate withholding revenue from the club, forcing an insolvency event to try and achieve their objective," Johnston told BBC Scotland.
Johnston, who admitted the timing of the ticket offer to Celtic fans was "regrettable" added: "You hope that people will realise that there's a football match on, with an 18,000-capacity stadium with more than 10,000 empty seats and we're trying to sell tickets for a football match to protect 200 employees at Rugby Park.
"My first obligation is towards the employees, which includes 42 professional footballers.
"The ringleaders of the angry fans have their own agenda and they are trying to force change with an objective of community ownership of the club.
"They don't care about the 200 employees we have here - I do - I'm trying to generate revenue, pay wages and keep people in employment in one of Scotland's biggest unemployment blackspots.
"I apologise for the timing of the announcements, because clearly that was a mistake, and that's highly regrettable, but the bottom line is that nobody was prejudiced by the offer made to Celtic supporters."
Killie boss Johnston insists the background bickering had nothing to do with the defeat.
He said: "No, we have just got to concentrate on the football.
"It is easy enough to make excuses and say that makes a difference but it is the football we have to concentrate on and it shouldn't affect the players.
"It is amazing to think we got beat 5-2 there. It was a really good performance but we lost cheap goals."
- Sports & Recreation
- Allan Johnston