Mark McGhee's men put in a professional performance to see off the Highland League side, but Dave Cormie's players battled hard throughout and generally gave a good account of themselves.
However John Sutton's brace which sandwiched one from David Clarkson proved more than enough to send the Scottish Premier League team through to a home tie against St Mirren in the last 16 on Saturday.
There was no Stephen Hughes in the Motherwell line-up, his place taken by Jim O'Brien, while Clarkson and Sutton continued up front after the departure of top scorer Chris Porter.
And it took just 90 seconds for Sutton to open the scoring, powering in a header from the impressive Keith Lasley's cross.
Locos responded when Mark Smith nodded down for Tommy Wilson, but his left-footed shot was comfortable for goalkeeper Graeme Smith, diving low to his right.
Well were dominant though, and Locos keeper Andy Reid had to look lively to turn a low Maros Klimpl shot past the post.
And when Clarkson's low cross-shot left Reid stranded, Scott Buchan positioned himself well to clear off the line.
The Locos defence were all too often being exposed by the clever play of their opponents, and Clarkson should have done better when he tamely gave possession away after beating the offside trap.
Mark Smith was impressing in midfield for the home side, and his ability helped them create a breakaway midway through the first half, however he ran out of options in the final third.
Clarkson's intelligent through-ball allowed Sutton another chance, but former Hibs goalkeeper Reid did well to block his shot as the conditions deteriorated.
Locos' best spell of pressure was to follow, with Smith, Wilson and Neil Gauld involved. However there seemed a reluctance to throw the ball into the box and the attack fizzled out.
With nine minutes remaining before the interval, what had been a competitive game took a nasty turn as a strong challenge led to a mass brawl, with Locos' Greig Pirie and Well's Stephen Craigan booked for their parts.
On the stroke of half-time, Reid again came to his side's rescue as he beat away a Sutton shot from 12 yards.
Locos came out fired up for the second half and four minutes in, Neil McLean cut in from the left and flashed a right-footed shot across goal.
The home side replaced Gauld with Danny Milne in a like-for-like swap, but it was a defender, Pirie, who caused problems for Well keeper Smith moments later as he challenged strongly for a corner kick.
However it was Motherwell who went further in front, this time from an O'Brien cross when Scotland international Clarkson rose highest to bullet his header beyond Reid.
That was to be the striker's last involvement as he was replaced by Under-21 cap Jamie Murphy shortly after.
Well midfielder Lasley was to become the third name in referee Willie Collum's book after a foul on Craig Ross, and he was quickly followed by Mark Simpson.
In between times, Wilson had seen a shot deflected wide for a corner, from which Pirie headed just wide.
The visitors made it three midway through the second half. A low cross from the right found its way across goal, and Sutton pounced to tap home his second of the night.
Locos made their final change when Than Tan Tran, a German of Vietnamese origin, replaced Ross, who was still suffering the effects of Lasley's earlier challenge.
With 15 minutes left, Reid rescued his side again when he saved from Murphy, and the goalkeeper went on to deny Sutton a hat-trick after Lasley's neat through ball.
It was a true man-of-the-match performance from the goalkeeper, who made another smart stop to deny Lasley with two minutes left.
Locos had a final chance to grab a consolation, but Milne hit over from the edge of the area after being played in by Tran.