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.
"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?"