Holders Barca had already reached the last 16 as group winners and Guardiola blooded a raft of recent youth-academy graduates in a starting lineup in which the 10 outfield players had an average age of just over 21.
Midfielder Sergi Roberto, 19, opened the scoring against the Belarusian champions in the 35th minute and full-back Martin Montoya (20) powered a shot high into the net for a 60th-minute second before Pedro (24) scored the third three minutes later with an audacious flick.
Pedro then converted a penalty two minutes from time after a foul on promising winger Isaac Cuenca (20).
Guardiola, himself a product of the club's 'La Masia' youth school, told a news conference the B-team on show at the Nou Camp, dubbed 'Baby Barca' in local media, had been "impeccable in every sense of the word".
"It's not easy fielding seven lads from the second team and giving the impression of playing well," added the former Barca and Spain midfielder, who rested most of the first team ahead of Saturday's opening La Liga 'Clasico' of the campaign at arch rivals Real Madrid.
"And it's not something that happens from one day to the next," he said.
"It's really nice that they were all able to participate and it makes us proud.
"They are talented players and I hope they can help Barca in the future."
Pedro, the only participant who could be considered a first-team regular, said Barca's second team was full of exciting young talent who were pressing hard for a permanent place with their senior colleagues.
"The quarry [youth academy] is very strong," the Spain forward, an academy graduate who is coming back from an injury layoff, told reporters.
"The players did a great job and they are coming through strongly and filled with desire to cement a place in the first team," the 2010 World Cup winner added.
