Leigh Griffiths netted a hat-trick after Efe Ambrose had given the Hoops the lead early in the second half, with Mikel Arruabarrena scoring for the home side.
Eibar had the best opportunities in the first half and Celtic ‘keeper Logan Bailly got down to his right to save a penalty kick from Dani Nieto moments after the midfielder’s shot was blocked by the outstretched arm of Dedryck Boyata on 26 minutes.
Four minutes later Boyata came to the goalkeeper’s rescue when Bailly completely fluffed his attempted clearance at the edge of the box, and the Celtic defender hooked the net-bound lob from Endika Arandilla clear.
Celtic looked much sharper after the break and James Forrest, whose progress was frequently halted by mistimed challenges in the opening period, won another free-kick 35 yards from goal four minutes into the second half.
Griffiths curled the set-piece towards the penalty spot and Ambrose timed his run to perfection to beat the hesitant Xabi Irureta with a downward header before producing his acrobatic celebration.
Celtic doubled the lead on 59 minutes when Griffiths smashed home a penalty off the inside of the ‘keeper’s left post after the striker had been brought down by Irureta as he tried to recover from fumbling the ball.
Eibar pulled a goal back nine minutes later when Emilio Izaguirre was harshly penalised when the ball struck his arm from close-range, and from the resulting spot-kick Arruabarrena beat Bailly with a neat chip.
Griffiths (74) restored Celtic’s two-goal advantage when he took a pass from Kieran Tierney on the right flank and fired a low shot into the net from around 25 yards which beat substitute ‘keeper Andoni Errasti at his near post.
And the Hoops striker completed his hat-trick in the dying seconds when he latched on to a 60-yard pass from Virgil van Dijk and strode into the box where he scored from a tight angle after Errasti had blocked his first shot.
Celtic looked considerably sharper in the second half of the match and they appear to be well prepared for their Champions League qualifier against Stjarnan in Iceland on Wednesday, with Ronny Deila’s side leading 2-0 from the first-leg.