The La Liga leaders, who defeated Real Madrid in last season's final to claim a record-extending 32nd Copa del Rey triumph, made eight changes from the side that beat Osasuna 2-0 at the weekend.
Hansi Flick's rotation was designed to protect a four-point lead over Real Madrid in the league, but it contributed to a disjointed first-half display.
Barcelona dominated possession, enjoying more than 80 per cent of the ball in the opening period, yet the first half ended goalless.
Eric Garcia came close to breaking the deadlock with an audacious effort from near the halfway line, which Guadalajara goalkeeper Dani Vicente almost parried into his own net. Despite sustained pressure, Marcus Rashford and Lamine Yamal made little impact before the interval.
The breakthrough finally arrived 14 minutes from full time when Andreas Christensen rose to meet a precise cross from Frenkie de Jong, heading home with Barcelona's 19th shot of the match.
The visitors sealed the contest in the 90th minute as England international Rashford, on loan from Manchester United and eager to secure a permanent move, rounded the goalkeeper and finished calmly after being released by Yamal.
"I was happy with the attitude we showed today. It was key for the victory too," said Flick.
"When you play this Copa del Rey games, it's not easy because they defended really good, but at the end, the most important thing is the attitude, the mentality we showed on the pitch, and it was good."
Marc Casado has reshaped his role at Barcelona as the midfielder battled to protect his place and earn minutes under head coach Hansi Flick, embracing versatility as competition across the squad intensified.
Kylian Mbappe scored twice as Real Madrid survived a major scare to beat third-tier Talavera 3-2 in the Copa del Rey round of 32 on Wednesday night.
Barcelona's veteran goalkeeper Marc-Andre ter Stegen faces a defining moment in his career as coach Hansi Flick places the decision about his future firmly in the goalkeeper's own hands ahead of the Copa del Rey tie with CD Guadalajara today.
A Raphinha brace was enough to help Barcelona to a 2-0 win over Osasuna at Camp Nou on Sunday to extend their lead at the top of LaLiga.
