Putellas, the UEFA women's player of the year who is a leading contender to win the Ballon d'Or later this month, converted the opening goal from the spot just before half-time in Germany.
Irene Paredes, Aitana Bonmati, Marta Torrejon and Ana-Maria Crnogorcevic all struck in the second half to secure a fourth win in four matches for Barcelona in Group C.
"I think we did a really good job," said Barcelona coach JonathanÂ Giraldez.
"We created many chances, and found the spaces inside. I think we didn't have the best clinical chances, but the overall performance from the whole team was amazing. We are really happy to have qualified for the next round."
Arsenal remain on course to advance from the same section after defeating Danish champions Koge 3-0.
Caitilin Foord gave Arsenal a first-half lead with Lotte Wubben-Moy and Vivianne Miedema grabbing late goals for the hosts at Meadow Park.Â
Record seven-time winners Lyon must wait to seal a place in the knockout phase following a 1-0 loss at Bayern.
Japan international Saki Kumagai headed in the winner midway through the second half to move Bayern to within two points of Group D leaders Lyon.
"I'm sad but proud of the team. It was a very difficult match, we fought a lot and had a lot of chances, right up until the last second, but we weren't able to take them," Lyon captain and goalkeeper Christiane Endler told DAZN.
"It's our first defeat of the season at the end of a very hard week with three big games, but that's not an excuse because Bayern have had the same schedule as us."
Benfica remain in contention for a spot in the last eight after scoring their first goals in the group stage in a 2-1 win away to Swedish club Hacken.
Standout matches today