The Hoops won on Italian soil for the first time with a 2-1 Europa League victory over Lazio in Rome on Thursday night and French striker Odsonne Edouard helped them take care of domestic duties with a 19th-minute opener at Parkhead
Well defender Richard Tait scored an own goal in the 54th minute to leave the home side ahead of Rangers, who won at Livingston by the same scoreline, by one goal scored.
It has been quite a few days for Neil Lennon and his side.
Celtic qualified for the last 32 of the Europa League with their win in the Stadio Olimpico with two Group E fixtures remaining and now they can now take stock during the international break still leading the table.
The start to the game, though, was in stark contrast to the end of the match in Rome.
Midfielder Olivier Ntcham, who scored the injury-time winner against Lazio after coming off the bench, was handed a start in place of Ryan Christie while 18-year-old full-back Jeremie Frimpong came in for the injured Hatem Abd Elhamed.
The visitors, without top-scorer Liam Donnelly and captain Peter Hartley through suspension and illness respectively, with Bevis Mugabi, Barry Maguire and Tait reinstated, were asked to do a lot of early defending but the home crowd was somewhat subdued.
Motherwell goalkeeper Mark Gillespie tipped a shot from Edouard round the post in the sixth minute for a corner which came to nothing.
However, the defender's luck deserted him for Celtic's first goal.
Elyounoussi slipped a pass into the box for James Forrest and after Gallagher challenged, the ball fell to Edouard and the 21-year-old guided it into the corner of the net past Gillespie for his 13th goal of the season.
Motherwell's occasional breaks carried danger.
Ntcham, Edouard and Elyounoussi all fired shots over the bar before Gillespie had to beat away a more accurate effort from Jonny Hayes.
It was from the Irishman's cross into the six-yard box, after a fine pass from Edouard which followed a good spell of possession, that Tait knocked the ball past Gillespie and into his own net.
With little left to lose Motherwell opened up and began playing more in Celtic's half, which stretched play.
In the 72nd minute Ntcham missed a great cross by Hayes but only by inches and then Gillespie saved a shot from the French midfielder at his near post before Celtic ran out comfortable winners.