Yacine Brahimi netted the only goal for Granada in the 16th minute before Barca spurned a host of chances, with Neymar taking a prime place among the culprits.
It is the second time this week Gerardo Martino's team have fallen by a 1-0 margin, following their UEFA Champions League exit at the hands of leaders Atletico Madrid – who have the chance to pull four points clear of the defending champions when they host Malaga tomorrow night.
There were no such problems for Real Madrid, who are now a point better off than their fierce Catalan rivals courtesy of a comfortable 4-0 home win over second-bottom Almeria.
Again operating without injured talisman Cristiano Ronaldo due to a knee injury, Real threatened to break the deadlock long before a 28th-minute opener from the impressive Angel Di Maria.
Gareth Bale, Isco and substitute Alvaro Morata completed the scoring on a significant night for Carlo Ancelotti's team.
Celta Vigo twice came from behind at home, despite being reduced to 10 men early in the second half, to claim a valuable 2-2 draw against Real Sociedad, easing their relegation fears.
The visitors twice hit the front through Sergio Canales and Antoine Griezmann, the latter's strike coming soon after Nolito's 37th-minute penalty.
Celta defender Jon Aurtenetxe then received his marching orders three minutes into the second half to put the home side under serious pressure but Santiago Min earned a share of the spoils in the 82nd minute.
That result meant Villarreal moved above Sociedad into sixth with a dramatic late win over Levante, while Celta rose to 12th with 37 points - five spots and six points clear of the relegation zone.
A 0-0 draw appeared on the cards at Villarreal's Camp El Madrigal until Jeremy Perbet headed home Manuel Trigueros' free-kick for the hosts in the fifth minute of stoppage time.