Bahrudin Atajic got off the mark for Celtic as Neil Lennon's side made it 12 goals in two matches since their European exit with a convincing Scottish Premiership win at Fir Park.
Celtic dominated throughout against a Motherwell side who failed to lift a sparse home support following their shock William Hill Scottish Cup defeat by Albion Rovers, as the visitors followed their 7-0 win at Hearts with a 5-0 triumph.
Kris Commons opened the scoring two minutes before half-time with a backheel and netted a rebound after Efe Ambrose had headed the second.
Anthony Stokes and Atajic finished the rout to send Celtic into their final Champions League game of the season in Barcelona on Tuesday on a high.
Motherwell manager Stuart McCall dropped James McFadden as he made five changes from the team that started arguably the worst result in the club's history, but they were poor again.
Calls from the Scottish Football Association to banish pyrotechnics were not heeded as a flare was lit in the Celtic end before a green smoke bomb was thrown on the pitch before the game.
There was a more positive display from that section as a banner of Nelson Mandela was held up as fans paid tribute to the former South African leader with a minute's applause.
Both sides lined up with three central defenders and two strikers but Celtic's midfield three of Scott Brown, Commons and Joe Ledley were more attack-minded and they played their way through the heart of the Motherwell defence inside 20 seconds but Gunnar Nielsen parried Mikael Lustig's shot.
Motherwell's difficult start continued when Fraser Kerr pulled up injured in the 10th minute. Adam Cummins came on.
Celtic continued to press and Mikael Lustig headed over from fellow wing-back Emilio Izaguirre's cross.
Motherwell managed to get the game moved further up the park but Joe Ledley found a gap in the home defence, however Teemu Pukki, who was in for the ill Nir Biton, lacked conviction and his shot was easily saved.
And Celtic took the lead after smart play from Izaguirre and Lustig opened up the home defence. Pukki's driven cross found Stokes at the far post and he fired a wayward shot that Commons flicked home with his back to goal from four yards.
Motherwell skipper Keith Lasley was booked for protesting in the aftermath of the goal, possibly about a free-kick he felt he should have had moments before. While the complaints continued, a missile thrown from the Celtic support flew over goalkeeper Fraser Forster's head and play was quickly halted after the restart when a green smoke bomb went off in his goalmouth.
Ledley and John Sutton headed just over at either end in the opening stages of the second half but Celtic doubled their lead in simple fashion in the 54th minute when Ambrose rose at the back post to head home a floated corner from Mulgrew, who had moved forward into a midfield diamond after the break.
There was to be no response from Motherwell as Celtic created a stream of chances. Lustig played in the overlapping Brown but Nielsen blocked before Stokes was foiled by the Faroes goalkeeper.
Pukki then shot over after being set up by Lustig before being booked for diving in the box despite appearing to be hurt by a Cummins challenge.
Nielsen saved from Ledley and then parried Izaguirre's curler in the 75th minute, only to see Commons bundle home the rebound.
Celtic broke a minute later with Pukki having yards of space on the right to send a low cross to Stokes to sweep home the fourth and Atajic calmly lobbed Nielsen in the final minute after being played through with no Motherwell player near him.