Strikes from Scott Sinclair, Moussa Dembele and Olivier Ntcham - plus an own goal - gave the Hoops a comfortable victory in Perth, in which every one of their outfield players aside from Scott Brown had a shot at goal.
The Parkhead side have broken their own mark, which stood at 62 games, that was achieved when Tom O'Malley's side enjoyed an undefeated run that began in 1915 and only ended in November 1917.
The run of the current side actually began with the last game of Ronny Deila's reign, when Motherwell were hammered 7-0 on the final day of the 2015-16 campaign.
Since then, former Liverpool boss Brendan Rodgers has been appointed and has yet to taste defeat in Scottish competition since taking charge of the side.
Indeed, only on a handful of occasions have Celtic come close to being beaten. Motherwell held a 2-0 advantage over them in December 2016 but were defeated 4-3, while late equalisers were required this term against both St Johnstone and Hibs to salvage a point in a couple of home matches.
HOW DOES CELTIC'S UNBEATEN RUN BREAK DOWN?
During their remarkable undefeated sequence, Celtic have won 55 matches, while in the league they have come out on top 44 times in 51 games.
Their cup record has been even more formidable, with 12 wins from 12 outings in the League Cup and the Scottish Cup combined. Aberdeen ran them the closest on this front, having only succumbed to a very late goal from Tom Rogic in last season's Scottish Cup final.
They have scored 183 over the course of these games, with Moussa Dembele grabbing 33. Hot on the heels of the France Under-21 international is Scott Sinclair, who has 30. Stuart Armstrong has contributed 20, while Leigh Griffiths has struck 19 times and Tom Rogic rounds out the top five with 14 goals.
At the other end of the field, meanwhile, they have conceded a paltry 35 goals. In these 63 games, they have kept a clean sheet on 36 occasions, with Craig Gordon credited with 35 of these and Dorus de Vries getting the other.