Brendan Rodgers's side equalled the 62-match mark last week with a draw at home to Kilmarnock but got back to winning ways, after a midweek Champions League defeat by Bayern Munich, with an easy victory.
Scott Sinclair, Moussa Dembele and Olivier Ntcham were all on target with Steven Anderson also scoring an own goal.
Celtic beat the previous record they shared with Willie Maley's Celtic side who went 62 unbeaten between 1915 and 1917.
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(Reporting by Martyn Herman; Editing by Toby Davis)
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