But it was Getafe who took a shock 39th-minute lead at the other end, with Damian Suarez's deep cross brilliantly chested back by Markel Bergara, allowing Shibasaki to unleash a magnificent 20-yard volley past Marc-Andre ter Stegen, who was making his 100th Barca appearance.
Ousmane Dembele hobbled off in the first half, as Barcelona came from a goal down to defeat Getafe 2-1 on Saturday.
After Barca failed to properly clear a Getafe free-kick, Shibasaki was on hand to absolutely thunder a ideal volley past Marc-Andre Ter Stegen and into the top corner.
Ter Stegen was also called into action in the ninth minute to gather a deflected strike from Faycal Fajr, before Gerard Pique picked up a booking for hauling Molina to the ground just outside the Barcelona box.
The opening 25 minutes of football passed without Barcelona having a single shot on target, and it got worse for the visitors when Dembele limped off the field with a hamstring injury on his first league start for the club, which saw Gerard Deulofeu introduced off the bench.
Gaku Shibasaki put the hosts ahead with a thunderbolt drive in the 39th minute.
Paulinho celebrates after his winning goal helps Barcelona beat Getafe 2-1.
Both teams continued to press for a victor but it was the visitors who managed to strike the decisive blow when Paulinho, who was brought on in the second half in place of Ivan Rakitic, drove into the box before firing a lovely finish across the keeper.
"I'm very happy to have scored the winning goal, it was very special", Paulinho said.
Former Tottenham midfielder Paulinho scored a late victor as Barcelona maintained their 100% record in La Liga by coming from behind to beat Getafe.