The Greece striker showed why manager Neil Lennon is looking to offer him a new contract with an impressive night's work albeit against a poor Caley side.
He notched either side of Gary Hooper's first competitive goal for the Hoops since signing from Scunthorpe in the summer to ensure the tie was all over by the interval.
Samaras, who also struck the bar in the first half, made sure of the match ball in the 57th minute when he showed commendable fighting spirit in the box before driving past Jonny Tuffey, whose performance actually prevented the score being even more demoralising for the visitors.
As the Highlanders crumbled further, Anthony Stokes scored from the spot in the 73rd minute, after he had been brought down by the Caley goalkeeper, before he drove in a wonderful 25-yard drive to complete the thrashing.
A decade ago Inverness, then a First Division side, had famously knocked Celtic out of the Scottish Cup at Parkhead, signalling the end of John Barnes' tenure as Hoops' boss.
The Highlanders repeated the feat on their own patch three years later but on this occasion the visitors were overwhelmed by Celtic despite Lennon making six changes to the side which beat Kilmarnock in the Clydesdale Bank Premier League on Sunday.
Most notably, fit-again striker Hooper was making his competitive debut while defender Mark Wilson started for the first time this season.
With the top tier of Celtic Park unopened due to lack of interest, the home side started sloppily and Ki Sung-Yueng needing to block a goal-bound shot from Nick Ross with only seconds on the clock, after the Hoops' defence had been split wide open by Shane Sutherland.
The home side got in to their stride and in the ninth minute Tuffey pulled off a fine save from Ki's 25-yard free-kick, after Grant Munro had clumsily bundled Hooper to the ground.
Moments later Hoops' defender Emilio Izaguirre limped off with what looked like a groin strain to be replaced by Charlie Mulgrew.
Celtic took the lead when Ki's corner from the right which was cleared to Ledley, whose first time drive was re-directed in to the net by Samaras from eight yards out, albeit the striker did not appear to know much about it.
Moments later the Greece striker was sent through on goal by Efrain Juarez but this time, with only Tuffey to beat, he crashed his shot off the bar.
But the former Manchester City player made amends soon after when he drilled the ball in to Hooper who turned at the edge of the six-yard box and volleyed past Tuffey for number two.
The tie looked settled even at that early stage but in the 31st minute, as the Hoops' defence went to sleep, Jonny Hayes fired in a shot from the edge of the box which came off Fraser Forster's legs.
But slick-moving Celtic stepped it up again and Juarez blazed the ball over the bar from close range after good work by Wilson on the right, before Tuffey made a good save with his foot from Anthony Stokes.
As the rain poured from the heavens, the floodgates opened in the Caley defence. In the 37th minute Samaras raced on to a Juarez pass to again leave the visiting defence flat-footed.
He clipped the ball over Tuffey rather too softly and was delighted to see it trundle over the line after Inverness defender David Proctor made a hash of his clearance.
Caley showed some spirit at the start of the second half but that was quenched when Samaras bounced Proctor off the ball inside the box before burying his low drive in to the corner of the net.
Stokes made it 5-0 from the spot after he had been felled by Tuffey inside the Caley box after racing through to take advantage of Munro's headed back pass which was too short.
The Irishman then scored the goal of the night with nine minutes remaining, driving powerfully from outside the box to give the flailing Tuffey no chance.