Through to the last 16 of the Champions League on their debut in the competition, Qatar-owned Malaga had lost three and drawn one of their previous five La Liga games but victory at the Rosaleda stadium gave them 25 points from 15 matches.
Real Betis also have 25 points in fifth spot ahead of Sunday's home game with leaders Barcelona while third-placed Real Madrid can narrow the gap on Tito Vilanova's men and Atletico Madrid with a win at Real Valladolid later on Saturday.
Unbeaten Barca, who have made a record start to the season, are six points clear of Atletico (34) with champions Real five behind their city rivals.
Granada, third from bottom on 12 points, made the livelier start on a treacherous pitch recently relaid after the grass was infected with a virus, and Malaga goalkeeper Willy Caballero had to rescue his side with a couple of fine saves in the opening minutes.
Former Spain winger Joaquin made it 1-0 in the 26th minute when he capitalised on a slip by defender Pape Diakhate and sped through the middle before finishing clinically.
Malaga fullback Jesus Gamez drove a long-range effort against the crossbar five minutes later before Saviola turned inside his marker and clipped a low shot into the corner to make it 2-0 in the 33rd.
The home team controlled the game in the second half and Camacho scored the third goal 15 minutes from time before substitute Santa Cruz volleyed in an 85th-minute fourth.
The match had an interesting sub plot as Malaga coach Manuel Pellegrini and Granada's Juan Antonio Anquela had last locked horns when Pellegrini's Real Madrid suffered a shock exit to Anquela's third-tier Alcorcon in the 2009 King's Cup.
Real Sociedad and Getafe exchanged late goals in a 1-1 draw at the Anoeta stadium in San Sebastian.
Getafe are sixth on 23 points and the Basques in eighth on 21.
Angel Lafita nodded in a Jaime Gavilan cross to put the visitors in front in the 86th minute but Carlos Martinez headed home from Alberto De La Bella's centre in the first minute of added time to rescue a point for Sociedad. (Reporting by Iain Rogers editing by Tony Jimenez)
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