Barcelona boss Ernesto Valverde made just the one change from the 3-0 win over Juventus on Tuesday night, with Sergi Roberto replacing Nelson Semedo at right-back. Ousmane Dembele started his first La Liga game alongside Luis Suarez and Lionel Messi in the final third, while Andres Iniesta kept his position in the team.
As for Getafe, Jorge Molina once again led the line for the capital outfit, while Japan international Shibasaki also kept his position in the team.
It was the home side that had the first half-chance of the match inside the opening two minutes, but Molina's effort from distance was gathered by Barcelona goalkeeper Marc-Andre ter Stegen.
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.
Getafe had a wonderful chance to take the lead in the 17th minute when a deflected Shibasaki cross fell for Molina at the far post, but the striker turned just the wrong side of the post as Barcelona survived another dangerous moment.
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.
It was the home side that took the lead in the 39th minute, however, when Shibasaki found the top corner with a stunning left-footed volley from the edge of the Barcelona box.
Messi thought that he had levelled the scores in first-half stoppage time with a sensational free kick, but Guaita made an outstanding save to ensure that the hosts would take a one-goal lead into the interval.
Denis Suarez replaced Iniesta as Barcelona made their second change ahead of the second period, but Getafe continued to resist the pressure as the hosts kept their lead intact entering the final 35 minutes of action.
Barcelona were pressing, however, and the visitors eventually levelled the scores in the 62nd minute when Denis Suarez, who had worked some space inside the Getafe box, found the top corner with a brilliant effort.
The visitors continued to dominate the possession approaching the final 15 minutes, but clear chances were few and far between as Getafe defended their own penalty box in impressive fashion.
Paulinho came off the Barcelona bench in the 77th minute as the league leaders looked to hurt Getafe late on, but it was the home side that almost scored 10 minutes from time, with Sergio Mora having a low shot deflected onto the post.
It was Paulinho that came up trumps in the 84th minute, however, with the Brazilian finding the far corner with a terrific finish to register his first Barcelona goal, which proved to be the difference on the afternoon.
Barcelona will attempt to make it five straight La Liga wins at the start of the new season when they welcome Eibar on Tuesday night, while next up for Getafe is a trip to Celta Vigo on Thursday.