Barca are third in the standings on 47 points, trailing leaders Atletico by eight points and second-placed Real Madrid by five points.
Eden Hazard scored his first goal in almost three months while Karim Benzema bagged a brace as Real Madrid eased to a 4-1 win away to Alaves.
The victory took Atletico on to 41 points after 16 games, four clear of second-placed Real Madrid who have played 18.
Lionel Messi and Antoine Griezmann each scored twice as Barcelona thrashed Granada 4-0 away to win a third consecutive La Liga game for the first time this season.
The win took Barca above Sevilla and into fifth place in the standings on 28 points, 10 behind leaders Atletico Madrid who beat Alaves 2-1 earlier on and who have a game in hand on the Catalans.
The win took the Spanish champions to the summit on 36 points, one ahead of second-placed Atletico who have three games in hand.
A Luis Suarez header gave Atletico Madrid a 1-0 home win over Getafe in coach Diego Simeone's 500th game in charge.
Martin Braithwaite missed a penalty for the Catalans.
A towering header from Casemiro and an added-time strike from Karim Benzema saw Real Madrid beat a stubborn Granada side 2-0 at home.
The Barcelona talisman scored his 644th goal to surpass Pele as the all-time record scorer for a single club.