Getafe celebrated after finding the back of the net following a shot from Jaime Mata, but their joy was short-lived with the match officials disallowing the effort for a foul in the build-up.
Barca took advantage of this to go in front courtesy of a nicely-poked finish from Lionel Messi, who kept his eye on a long ball before finishing into the bottom corner on 20 minutes.
Defender Gerard Pique showed attacking instincts when he propped up inside the box to meet a cross from Messi on goal, but David Soria palmed the effort out for a corner on 27 minutes.
Uruguayan Luis Suarez brought a low ball comfortably into his path to get a curling strike away, but the final delivery failed to creep into the bottom corner after a few minutes.
On 38 minutes, Suarez displayed redemption at the perfect juncture as he volleyed home a second-ball from the edge of the box to double Barca's lead.
Minutes later, Getafe nearly carved out a response when a cross into the box deflected off Arturo Vidal and onto the post following a snap-shot on the volley.
The Catalans were finally caught out as Mata arrived at the right place and time to cut the deficit following a good delivery by Angel three minutes to the break.
The home side started the second half in a lively sphere, and nearly grabbed the equaliser after Angel latched on to a loose ball inside the box to send a shot narrowly wide of goal.
Barca’s goalkeeper Marc Andre Ter Stegen was called to action as he send Mata’s header following a corner over the top midway through the second half.
The five-time European champions continued living dangerously, as Mata was unfortunate not to guide home from a gaping net after slicing through the entire defence towards the final quarter.
Soria kept their hopes of a draw alive by narrowing down the angle on Messi’s low shot from inside the box before stopping the ball with his right-hand inside the final 15 minutes.
In the closing stages, Messi had another go at Soria to try and complete his brace, but the latter once again made his presence felt with a one-handed save on this occasion, with Dembele skewing the follow-up back into play as the encounter finish 2-1 in favour of the visitors.
With this result, Barca have opened up a five-point gap over second-place Atletico Madrid, who dropped points against Sevilla earlier on Sunday.