Barca are now second on 66 points, two behind Real who have a game in hand as they chase a first title triumph since 2012.
Luis Suarez rose to the challenge that Lionel Messi's absence provided by powering second-placed Barcelona to a hard-fought 4-1 win at struggling Granada on Sunday after La Liga leaders Real Madrid laboured to a 3-0 victory over Alaves.
The Uruguay striker scored Barca's opener with a classy lob in the 44th minute and provided assists for Paco Alcacer and Ivan Rakitic to seal the points after the home side surprisingly drew level early in the second half through Jeremie Boga.
Neymar added extra shine to the victory with his 100th goal for Barca by knocking in a cross from Alcacer in added time.
"It's great when you can make up for absences with the type of squad we have, because it is squads that win you trophies," Barceona coach Luis Enrique told reporters.
"The game became complicated with their equaliser in their only chance of the game but we managed to turn it around quickly and get a big scoreline which I think is a fair result."
Sevilla slipped out of the top three after being held 0-0 at home by struggling Sporting Gijon in the early game.
Barca are second on 66 points, two behind Real who have a game in hand as they chase a first title triumph since 2012. Atletico are third above Sevilla, who also have 58 points.
La Liga top scorer Messi was suspended for Barca's trip to the picturesque Andalusian city, where they clinched the title last season, and Luis Enrique took a risk by resting regulars Gerard Pique, Andres Iniesta and Samuel Umtiti before losing Rafinha to injury in the 17th minute.
The visitors dominated but took 44 minutes to open the scoring when Suarez calmly chipped Jordi Alba's sumptuous through ball over goalkeeper Guillermo Ochoa to finally get the better of the Mexican.
Boga grabbed an equaliser five minutes after the break for second-bottom Granada and Luis Enrique's rotations suddenly looked misguided before Suarez got them out of jail.
He teed up Alcacer in the 64th and then provided a pass to Rakitic which was deflected in off Matthieu Saunier just after Granada's Uche Agbo was sent off for a second booking.
Neymar rounded off the victory with his milestone goal.
