Livi were no match for the League leaders after a powerful first half Hoops’ performance effectively tied the result up.
Ange Postecoglou’s side blitzed their visitors in the first half, with Greg Taylor netting the first with a sweet strike across the deck and Daizen Maeda and Kyogo Furuhashi both converting one of a plethora of chances.
The onslaught eased after the break but Celtic strolled to victory, with Livingston’s only real threat coming when Bruce Anderson struck the woodwork from an acute angle.
Celtic absolutely smothered their visitors. This was a fantastic, unrelenting display, particularly first half, which ought to have brought more goals.
Livingston struggled to hold any possession at all, never mind creep up the pitch to threaten other than one moment in the first half.
It was a one-way street for Celtic, a direct result of them dominating the ball but winning it back instantaneously if they lost it. That was rare.The first threat came when Jota tried to thread the ball in front of the onrushing Kyogo, but the ball carried a touch too much weight.
The Portuguese winger then somehow contrived to miss from a few yards when Maeda showed brilliant pace and poise to flash the ball across the six-yard box but there was no connection with the goal gaping.
Just when you thought Livingston were about to frustrate their hosts, Reo Hatate gathered in the box, laid it back to the onrushing Taylor, in a now familiar advanced inside-left position, and he fired across Shamal George into the corner.
The second followed quickly. Livingston just could not get a decisive clearance and when they finally tried one, the ball cannoned off the onrushing Maeda and home. His persistence paid off and Celtic were off and running.
Livingston did manage one scare on the almost anonymous Joe Hart’s goal when Anderson seized on a slip, but his shot cracked a post and the follow up fell wide. There ended Livingston’s threat and any hope of a revival.
Celtic’s third was as simple as inevitable. Matt O’Riley launched an accurate ball upfield for Kyogo. He had Jack Fitzwater for company, but bobbed and weaved towards the box before placing his 21st goal of the season into the net.
The second half was a procession that lacked the killer touch with Celtic constantly probing and Livingston staying stoic in adversity.
They held firm to stop more damage with the result determined in the opening 45.
Match Report: Martin Dowden (BBC)
Celtic: Hart, Johnston, Carter-Vickers, Starfelt, Taylor, McGregor © (Iwata 85), Hatate (Turnbull 75), O’Riley (Abada 63), Jota (Mooy 63), Maeda ▊, Furuhashi (Oh 75)
Subs not used: Bain, Kaksabanovic, Kobayashi, Forrest
Goals: Taylor (29), Maeda (33), Furuhashi (45)s
Livingston: George, Devlin © ▊ (Montaño 57), Fitzwater, Obileye, Boyes, Penrice, Omeonga (St.Kelly 69), Holt, Shinnie (Bradley 81), Pittman, Anderson (Nouble 69)
Subs not used: Hamilton, de Lucas, Longridge, Sn.Kelly, Guthrie
Referee: Nick Walsh