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.
But two substitutes, Suarez and Paulinho, both struck after the break as Ernesto Valverde's men continued to set the pace at the top of the table.
Dembele, Barcelona's record signing, had started against Juventus in the club's 3-0 Champions League win on Tuesday.
Barca's fine start to the season means they already sit seven points clear of reigning champions Real Madrid, whose game in hand is a testing away trip to in-form Real Sociedad on Sunday.
"We have shown that we can come back", he said.
In the 16th minute Getafe squandered a great opportunity to grab the lead after Molina failed to connect to Baku Shibasaki's deflected cross.
Getafe hero Shibasaki had to leave the match with an injury of his own early in the second half, shortly before Sergi Roberto tested Guaita.
The France winger who an initial €105million, was making his first La Liga start for the Catalans, picked up a hamstring injury and was replaced by Gerard Deulofeu.
Luis Suarez had a penalty claim turned down after tangling with Djene Dakonam in the box, ultimately earning himself a booking after continuous dissent. He also brought a great save out of Getafe goalkeeper Vicente Guaita with a wicked free-kick, and nearly scored after Paulinho, seeing a shot deflect wide.
Barcelona completed the comeback vs. Getafe and remain flawless in La Liga courtesy of new-signing Paulinho's strike late on.