McHugh headed the visitors into an early lead, and McFadden added a second with a delightful backheel to send Motherwell into the fourth round of the Scottish League Cup.
Livingston grabbed a late consolation through Danny Denholm despite being reduced to 10 men after Jason Talbot incurred a straight red card for a reckless two-footed lunge on Stevie Hemmell.
Motherwell boss McCall said: "I have to say, I thought Livingston were terrific and it was only really when they went down to 10 men that we had chances to kill it off.
"I think we did enough to win the game. I'm disappointed to lose the goal but overall we're in the next round and that's the main thing.
"The park was really wet and it was skidding off and things weren't coming off in the final third for both teams, but I'm pleased James got on the scoresheet and got a full 90 minutes.
"He is desperate to do well, he puts everything into training and games.
"Both strikers scored so that was great."
Livi boss John McGlynn had issues with the sending off of Talbot, but he was pleased with his side's performance overall.
"I would need to see it again but I don't think you need to go in as aggressively in that position on the pitch. Away up there, what danger is anyone doing to you?
"It cost us because we were well in the game."
"I thought we played some really good football and controlled large chunks of the game. Credit to the lads, we even got a goal back at the end."