The holders had comfortably reached the last 16 as group winners last month and coach Pep Guardiola blooded a slew of recent youth-team graduates in a starting lineup in which the 10 outfield players had an average age of 21.4.
Teenage midfielder Sergi Roberto opened the scoring against the Belarussian champions in the 35th minute when he stroked a loose ball low past goalkeeper Aleksandar Gutor.
Full-back Martin Montoya powered a shot high into the net for a 60th-minute second before Pedro scored the third three minutes later with an audacious flick and then converted a penalty two minutes from time after a foul on winger Isaac Cuenca.
Barca's tally of 20 goals in their six group games equalled the record set by Manchester United in the 1998/99 season as the Catalan club seek a fifth triumph in Europe's elite club competition and a third in four years.
"Having this generation of players and being able to depend on them is very valuable," a delighted Guardiola, marking his 150th victory in his 208th match as Barca coach, said in an interview with Spanish television.
"The difficult thing for them now will be maintaining this level when they go back to playing at second-division stadiums [for Barcelona B]," added the former Barca and Spain midfielder, himself a product of the club's 'La Masia' youth school.
"But I am very proud of them," he said.
'CLASICO' LOOMING
Guardiola had the luxury of being able to rest most of his first-choice players with Saturday's opening La Liga 'Clasico' of the season at great rivals Real Madrid looming.
World Player of the Year Lionel Messi, playmakers Xavi, Andres Iniesta and Cesc Fabregas and keeper Victor Valdes were all left out of the squad and Spain forward Pedro was the only player in the starting XI who could be considered a regular.
Tuesday's side, dubbed 'Baby Barca' in local media, included brothers Thiago Alcantara, 20, and 18-year-old Rafinha, whose Brazilian father Mazinho played professionally in Italy and Spain.
Emulating their senior team-mates watching from the stands, the youngsters seized control of possession from the kick-off and Rafinha went close in the second minute with a strike from an acute angle that Gutor blocked with an arm.
The promising Cuenca has shone on several previous appearances for the first team and it was his delicate pass that sent Montoya clear for Barca's second and his low cross that created their third and the first of Pedro's two goals.
Cuenca also won the late penalty in a man-of-the-match performance that suggested he has a bright future.
"Winning 4-0 against a top-level Champions League opponent is a reason for great joy for all of us," first goalscorer Sergi said.
"A bunch of players from the youth school were playing tonight and for me that is fantastic," the 19-year-old added.
"Most of us on the pitch were from the B-team and you could see that in the understanding we ha
