For only the fourth time in their history the Reds scored five in a European away tie, the last of which came against Finnish side Haka in a 2001 Champions League qualifier.
Jonjo Shelvey, a 67th-minute substitute, stood out with two strikes while 19-year-old Andre Wisdom marked his senior debut with a header and Sebastian Coates and an Juhani Ojala own goal rounded off the scoring.
Liverpool looked fragile as they slipped from 2-1 up to 3-2 down after Ojala and Gonzalo Zarate had added to Nuzzolo’s first-half equaliser.
With the first team having scored just nine goals in eight matches Rodgers’ second-string, which included three debutants, found scoring much easier.
“We have come away with a young team into a European game and I want to talk about the five goals we scored which were absolutely magnificent,” said Rodgers.
“Of course we could have defended better and there is no question the three goals we gave away were disappointing.
“But to draw positives from tonight the young players were so courageous and brave to play and show that confidence, and my senior players were very much together and kept the young guys going.”
Rodgers also had praise for Shelvey, making his 45th appearance for the senior side, and predicted a bright future for the England U21 international.
“I felt it was the time of the game we needed him really,” he said of Shelvey’s second-half introduction.
“He has been outstanding. He is still only 20 years of age and is developing and growing all the time and you saw his confidence when he came on. I think he will be a big player for Liverpool.”
Young Boys’ coach Martin Rueda bemoaned the errors by his side, starting with a comical fourth-minute concession when Dusan Veskovac headed against team-mate Ojala to beat goalkeeper Marco Wolfli.
He said: “We made too many individual mistakes and that cost us the match. If you make a mistake you immediately get penalised at this level.”
YOUNG BOYS: Wolfli, Spycher, Ojala, Zverotic (Frey 81), Sutter, Veskovac, Raimondi, Nuzzolo (Schneuwly 69), Farnerud, Zarate (Gonzalez 65), Bobadilla.
LIVERPOOL: Jones, Carragher, Enrique, Wisdom, Coates, Sahin, Henderson, Downing (Sterling 77), Pacheco (Borini 62), Assaidi (Shelvey 67), Suso.
Ref: Michalis Koukoulakis (Gre).