Victory at Fir Park saw Celtic go two points ahead of Rangers after their arch Glasgow rivals won 3-1 at home to Kilmarnock on Saturday.
Fir Park was the scene for a dramatic late win that helped Celtic claim last season's title and Sunday's success came after a fractious three-week international break that saw club owner Dermot Desmond subjected to a tennis-ball protest by irate fans at St Andrews golf course last weekend, as well as uncertainty over the future of manager Martin O'Neill.
But Camilo Duran's early goal on Sunday helped improve the mood among the Hoops' faithful before Celtic doubled their lead through Benjamin Nygren in the 58th minute as they made it seven wins in eight league matches this term.
Nevertheless, banners and chants criticising Desmond were seen and heard at Motherwell.
But it was home fans who were seen leaving Fir Park early as their uninspiring side suffered a fourth successive defeat.
