Jeremy Mathieu was the sole survivor in Barca's starting XI from Sunday's 1-0 Liga victory at Valencia, but Luis Enrique's makeshift side showed the gulf in class between the two teams in the first leg at the Estadio El Alcoraz.
Ivan Rakitic was the driving force in Barca's midfield and his tremendous free-kick opened the scoring, before Andres Iniesta - playing his first match since October 25 due to a calf injury - grabbed his first goal of the season with an excellent finish.
Pedro effectively ended the game as contest with a fierce drive seven minutes before the break, and Rafinha made it four in the second half with his first Barca goal - albeit with the help of a huge deflection.
The two teams will meet again on December 16 at Camp Nou, when there will surely be no way back for the Segunda B side after Barca's ruthless first-leg display.
Unsurprisingly Barca started on the front foot, but goalkeeper Marc-Andre ter Stegen got lucky with a clearance that struck Guillem Marti Misut and almost crept in.
That proved a momentary blip, though, and Rakitic opened the scoring when he bent a sublime 25-yard free-kick into the top right-hand corner in the 12th minute.
It took just three minutes for the visitors to double the lead, as a swift five-on-three break eventually resulted in Rakitic picking out Iniesta on the edge of the box and he showed excellent technique with a crisp outside-of-the-boot finish.
Huesca were enjoying some success in wide areas and Juanjo Camacho's excellent centre from the left picked out Guillem, whose side-footed shot was saved by the feet of Ter Stegen on the half-hour mark.
Shortly after Rakitic came desperately close to a second with another free-kick that rattled the post, but Barca did extend the lead seven minutes before the break when Pedro cut in from the left and hit a stinging shot inside Dani Jimenez's near post.
The hosts showed plenty of grit after the break, with Guillem coming close when he bent a shot wide of Ter Stegen's left-hand post before testing the German with a shot from distance.
Barca's pace in attack remained a constant threat, though, and Pedro wasted a great chance to add his second goal when he fired high and wide from the right of the box.
A fourth arrived with more than a hint of fortune in the 71st minute, as Rafinha broke his Barca duck via a huge deflection that left Jimenez helpless.
The home side almost grabbed a consolation in the closing stages when a goalmouth scramble led to chances for Guillem and Juan Esnaider, while Chus Sosa volleyed over from a promising position but Barca were not to be denied a clean sheet.
