Former Hearts star Aidan Keena came back to haunt Motherwell as he provided Sligo Rovers with a slender lead to take to Ireland in their Europa Conference League second qualifying round.
Keena struck in 27 minutes when he pounced on Mugabi's slack passback and lobbed the ball over Kelly and into the net.
It was no more than the visitors deserved by that point, having threatened a few times, while Motherwell didn't create much up front, though Blair Spittal and Kevin van Veen went close ahead of the interval.
Sligo disappeared somewhat after their goal, though they popped up on occasions to remind the Steelmen that there was a definite threat there.
Though Josh Morris was unlucky with a free kick in the second half, and Callum Slattery saw a fierce shot well saved, Motherwell just didn't do enough to test Rovers.
They were maybe given a late let-off too, as Jake Carroll appeared to handle a Max Mata header on the line.
Motherwell boss Graham Alexander started all three of his new signings in Paul McGinn, Blair Spittal and Josh Morris, while striker Kevin van Veen took his place up front.
His Sligo Rovers counterpart John Russell made three changes from their 2-0 defeat against University College Dublin on Sunday. In came Karl O'Sullivan, Adam McDonnell and Gerry Buckley, for Nando Pijnaker, Frank Liivak and Max Mata, who were all on the bench.
Sligo created the first chance of the game and inside the opening minute William Fitzgerald blasted over at the right post.
At the other end, Morris rippled the left side-netting with a shot in three minutes.
Sligo went close again in eight minutes when Buckley's cross from the left was met on the volley by Lewis Banks, but Liam Kelly made a smart save on the line.
Former Hearts and Dunfermline star Aidan Keena tried his luck with a shot from distance in 19 minutes, but his ambitious effort was comfortably taken by Kelly.
Motherwell were nearly gifted the opener in 21 minutes when a slack passback by Paddy Kirk let van Veen through on the right, and his shot was blocked by keeper Luke McNicholas, but landed just too far ahead of Morris, and his effort was also repelled.
Sligo took the lead in 27 minutes when Mugabi was short with a passback and Keena raced onto it before lobbing the ball over Kelly and into the net.
Barry Maguire had a drive brilliantly pushed past the left post by McNicholas in 35 minutes.
And van Veen should have drawn them level just before the interval, but fired wide from close distance.
The Dutch striker nearly levelled for the hosts just after the restart, but McNicholas came out well to clear the danger with his feet.
Morris curled a free kick towards the top right corner in 58 minutes, but McNicholas was equal to it.
Rovers could have doubled their lead just before the hour-mark when Karl O'Sullivan crossed for Fitzgerald at the left post, but he headed high and wide.
Motherwell should have drawn level in 71 minutes when Spittal sent sub Ross Tierney through on the left, but the striker could only find the side-netting.
Callum Slattery tested McNicholas with a drive in 73 minutes, but the keeper parried before the danger was cleared.
Mugabi tried to make amends for his earlier error but sent his header narrowly wide of the left post from a Slattery free kick in 79 minutes.
Motherwell were given a let-off in 84 minutes when sub Max Mata's header appeared to be handled on the line by Carroll, but a corner was given.
The Steelmen could have snatched a leveller late on, but Morris' header was brilliantly saved by McNicholas at the right post corner.
MOTHERWELL: Kelly, McGinn, Lamie, Mugabi, Carroll, Maguire, Slattery, Spittal (Efford, 74), van Veen, Morris, Shields (Tierney, 65).
Subs (not used): Fox (GK), Kennedy (GK), O'Donnell, Solholm, Cornelius, Goss, Mahon, Campbell.
Booked: Carroll (7), Maguie (66)
SLIGO ROVERS: McNicholas, Banks, O'Sullivan, Blaney, Kirk, McDonnell (Mata, 77), Morahan, Cawley, Fitzgerald, Buckley, Keena.
Subs (not used): Brush (GK), Vahey (GK), McCourt, Liivak, Byrne, Heaney, Pijnaker, Barlow, Clancy, McCarthy.
Booked: Blaney (14), Banks (74)
Referee: Kari Hovdanum.
Attendance: 7227.
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