Trouble returned to Real Madrid after they endured their first La Liga defeat of the season at newly-promoted Real Mallorca.
Barcelona are second in the La Liga table, two points behind Real Madrid, following their 4-0 win over Sevilla at Camp Nou.
Barcelona came from behind to beat Inter Milan in a thrilling Champions League contest at Camp Nou on Wednesday.
Granada vs Barcelona: With seven points on the board, this is Barcelona's worst start to a season since 1994.
Lionel Messi and Luis Suarez were in the stands as Barcelona beat Real Betis 5-2 at Camp Nou on Sunday.
Substitute Aritz Aduriz scored a sensational late volley as Athletic Bilbao beat Barcelona 1-0 in La Liga's first match of the new season.
Luis Suarez scored the winner in the 89th minute in front of nearly 99,000 people, who packed the stands to see new signings Antoine Griezmann and Frenkie De Jong.
Lionel Messi, who turns 32 in June, Sergio Busquets, who will be 31 in July, and Gerard Pique, already 32, have hung on, driving the club through fresh cycles of success.
Luis Suarez had bit Italian centre-back Giorgio Chiellini on his shoulder in World Cup 2014.
With Barcelona's focus clearly on Manchester United, Lionel Messi and Gerard Pique were among 10 players rested for the goalless draw against Huesca.
Barcelona broke the resistance of 10-man Atletico Madrid on Saturday to go 11 points clear of their La Liga title rivals.
Lionel Messi's treble, his second in a month in Seville, fourth of the season and 51st of his career, moves Barcelona 10 points clear of Atletico Madrid.
Rayo took the surprise lead at the Camp Nou but Lionel Messi converted a penalty and Luis Suarez finished a brilliant passing move to seal a 3-1 win.
Barcelona have now gone six away matches without winning in the Champions League knockout rounds, scoring just a single goal in that time.
Lionel Messi netted his 31st La Liga hat-trick as Barcelona regained their three-point lead at the top of the table.
Philippe Coutinho scored the first and Arturo Vidal the last but in between the game belonged to Luis Suarez.
Lionel Messi scored a hat-trick as Barcelona put four goals past PSV Eindhoven in the Champions League.