The final at the Almondvale Stadium flattered the home side, who were on the back foot for the majority of a tie they finished with 10 men after Jason Talbot was sent off for a rash challenge on Steven Hammell.
Motherwell asserted themselves from the outset and carved out a fourth-minute chance for McHugh, whose tame effort was easily held by Darren Jamieson.
But the visitors were ahead in the 16th minute as Lionel Ainsworth’s corner was flicked on by Simon Ramsden, and McHugh ghosted in to nod home from a yard out.
Ainsworth came close to celebrating his first Motherwell start with a goal as his full-blooded drive forced a superb finger-tip save from the home goalkeeper.
McFadden had a penalty appeal waved away went he went to ground after tangling with Coll Donaldson as a disappointing first half petered out.
The former Scotland striker failed to convert the first chance of the second half after excellent work from strike-partner McHugh, who drilled wastefully over the bar moments later.
Livingston then enjoyed their best spell of the game as Marc McNulty’s powerful effort fizzed inches wide before Andrew Barrowman’s header grazed the outside of the post.
But the home side’s hopes of finding an equaliser took a significant hit on 65 minutes as Talbot’s reckless two-footed lunge on Hammell earned him a straight red card – the ninth of his career.
Motherwell then put the result beyond doubt in the 73rd minute thanks to a touch of class from McFadden, whose exquisite backheel from Ramsden’s cross gave Jamieson no chance.
McFadden almost grabbed a second when his follow-up was deflected over the bar after Jamieson beat away Ramsden’s shot, and the busy home keeper did well to keep out another Ainsworth shot.
Danny Denholn bundled home from close-range after Martin Scott’s corner bounced through a host of bodies, but it came too late to spark a home comeback.