The result ensured that the Catalans stay clear of Arsenal at the top of Group C, while seven-time Champions League winners Lyon are five points clear in Group D after coming from behind to beat closest rivals Bayern Munich 2-1.
Jennifer Hermoso headed Barcelona into a fifth-minute lead against Hoffenheim and Putellas smashed in a left-foot free-kick from 20 metres to make it 2-0 before the midway point in the first half.
Putellas, the UEFA women's player of the year who is a leading contender to win the Ballon d'Or later this month, made it 3-0 just after the half-hour mark, her shot dribbling through the legs of goalkeeper Martina Tufekovic.
Marta Torrejon headed in a Putellas cross to complete the rout in the 74th minute, shortly after the floodlights briefly went out at the Johan Cruyff Stadium.
Barcelona, whose coach Jonatan Giraldez is not yet 30, maintain their 100 percent record in Group C and have 12 wins out of 12 in all competitions this season, with 64 goals scored and just three conceded.
Arsenal sit second in their section on six points after cruising to a 5-1 victory away to Danish champions Koge.
The English WSL leaders saw Nikita Parris have an early penalty saved but they went ahead in the 27th minute when Australia's Steph Catley curled in a free-kick in front of the sizeable travelling support.
Parris made it 2-0 just after the hour mark and Caitlin Foord, another Australian international, headed in the third after captain Jordan Nobbs hit the bar.
American Maddie Pokorny pounced on a Catley mistake to pull one back for the hosts just outside Copenhagen, but substitute Anna Patten made it 4-1 and Nobbs completed the rout.
Lyon, who won the trophy five years running from 2016 to 2020, fell behind at home to German champions Bayern when Canada's Kadeisha Buchanan put through her own net under pressure from Carina Wenninger.
However, Belgian international Janice Cayman equalised from close range early in the second half and Amandine Henry headed in an 86th-minute winner.
In the same group a late Elin Rubensson penalty gave Swedish champions Haecken a 1-0 victory away at Benfica.
Lyon have nine points, five more than Bayern and six more than Haecken.
On Tuesday, last season's runners-up Chelsea crushed Servette 7-0 in Switzerland to move two points clear at the top of Group A from Wolfsburg, who drew 2-2 at Juventus.
Paris Saint-Germain beat Real Madrid 4-0 to make it three wins out of three in Group B.