With tougher games against Aberdeen and Villarreal coming up, Celtic boss Gordon Strachan made full use of his rotation system making seven changes but a Paul Caddis cross after 23 minutes gave the Hoops a first-half lead against the Irn-Bru First Division leaders who, despite being neat and tidy at times, never looked like producing a shock.
Greece international Samaras showed why he has established himself Celtic’s as number one striker this season after making his loan deal from Manchester City permanent when he added a second just after the hour mark, heading home from close range after being set up by Loovens.
With 10 minutes remaining, Samaras turned provider for Scott Brown, on for Massimo Donati, to grab the third and there was still time for the Greek to score his second from the spot after Shaun Maloney, who had replaced Scott McDonald, was tripped in the box by Livi defender Dave Mackay.
Meanwhile, Dundee United eased into the quarter-finals of the Co-Operative Insurance Cup with a 2-0 win over Airdrie.
The Diamonds could not repeat the giant-killing feat which saw them dump Hearts out at the last stage and were outclassed by Craig Levein’s men.
Striker David Goodwillie opened the scoring on 32 minutes before Scott Robertson secured the victory with a stunning strike 10 minutes later to send last season’s finalists into the last eight.
CELTIC: Boruc, Hinkel, Naylor, McManus, Loovens, McGeady, McDonald (Maloney 77), Donati (Brown 63) Samaras, Caddis, Hartley
LIVINGSTON: McKenzie, Mackay, Talbot (Miller 73), McPake, Fox (Giarrizzo 60), Innes, McParland, Davidson, Elliot (Cuenca, 54), Quinn, Hamill
Referee: W Collum (Scotland)