Paulinho who arrived at the Camp Nou this summer, came off the bench to net the victor, to ensure their ideal start to the season continues.
The visitors lost Ousmane Dembele to injury in the opening period of his full Liga debut and their Saturday afternoon got worse when Japan worldwide Gaku Shibasaki scored his first Getafe goal in stunning fashion before the break.
Dembele, Barcelona's record signing, had started against Juventus in the club's 3-0 Champions League win on Tuesday.
Getafe, which has won only one of its four games, led through Japanese midfielder Gaku Shibasaki just before halftime.
Roberto shows great tenacity down the right before cutting the ball back into the box for Suarez who came on at the start of the second half for Andres Iniesta.
In first half stoppage time Guaita produced a good save to turn Lionel Messi's free kick away for a corner.
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 in tact entering the final 35 minutes of action.
Luis Suarez had a penalty claim turned down after tangling with Djene Dakonam in the box, ultimately earning himself a booking after continuous dissent.
Barcelona completed the comeback vs. Getafe and remain ideal in La Liga courtesy of new-signing Paulinho's strike late on.
Valverde introduced Paulinho in his final change, but it was Getafe who nearly grabbed a shock victor when Mauro Arambarri's deflected effort bounced off the foot of the post.