REO HATATE has so far been unable to play a huge part in Celtic's bid for this term's title.
But the Japanese star is back at just the right time for Brendan Rodgers.
Hatate has suffered a series of injury setbacks which have wrecked his campaign but with only seven games to go, he might still have a pivotal say.
Hatate made a first start in five months but looked as if he'd never been away with a terrific showing.
Full of energy and invention for his 64 minutes, the midfielder topped the performance with the strike that led to Jamie Brandon's own-goal opener.
Replaced by Paulo Bernardo, the Portuguese made the alteration seamless as his fourth goal of the campaign sealed the deal before Matt O'Riley's 12th of the term completed a midfield-scoring masterclass.
Rodgers was stuck in the stand serving his suspension but there was no sign of his Celtic side getting stuck on the artificial pitch as they surged back to the peak of the Premiership.
In lashing Livingston, they have set themselves up perfectly for Sunday's blockbuster against Rangers.
A potentially tricky afternoon was overcome as more pain was inflicted onto David Martindale.
Livi are cut adrift and with 10 points the deficit to 11th-placed Ross County, the situation is beyond grim in terms of survival.
Celtic though have their eyes on the big prize. And although they had to wait until the second half to make the breakthrough, they were in control throughout. Their sense of urgency and intent was evident. Hatate set the tone with a first drive over after an O'Riley corner found him.
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