Leaders Barcelona extended their unbeaten run to 28 games – equalling a club record – and moved three points clear at the top of the Primera Liga with a laboured 2-0 win over bottom side Levante.
Barca’s opener came when David Navarro turned into his own net after 21 minutes and it was not until Luis Suarez struck in injury time that victory was certain.
Levante made life tough and went close on a number of occasions, notably when Jose Luis Morales hit the woodwork.
Modric struck from outside the box five minutes from time to settle Madrid nerves after substitute Youssef El-Arabi had pulled Granada level on the hour.
El-Arabi had been on the field just two minutes when he cancelled out Karim Benzema’s 30th-minute opener.
Gary Neville’s future as Valencia manager hung in the balance after his side suffered another disappointing result with a 1-0 loss at Real Betis.
The former Manchester United defender is yet to taste victory in nine league matches, with his side’s latest reverse being their fourth defeat in those matches since he took charge.
Ruben Castro scored the only goal at Estadio Benito Villamarin, with Valencia’s woes compounded by the late sending off of Jose Luis Gaya and the ruling out of a headed injury-time equaliser from Shkrodan Mustafi.
The result left Valencia – thrashed 7-0 by Barcelona in the Copa del Rey in midweek – just four points above the relegation zone.
Federico Fazio – sent off on his first Premier League appearance for Tottenham last season – received another debut red card for Sevilla in their 1-1 draw at Celta Vigo.
The defender, who rejoined the club on loan from Spurs earlier in the week, was dismissed for two bookable offences inside the opening 24 minutes.
Sevilla, who thrashed the same opponents 4-0 in the first leg of their Copa del Rey semi-final, responded well to score through Daniel Carrico, but Claudio Beauvue claimed a deserved point for the hosts.
On Saturday, Fernando Torres brought up a century of goals for his boyhood club as Atletico Madrid beat Eibar 3-1.
Former Atletico academy player Keko gave the visitors a surprise lead at the start of the second half following an error by Saul Niguez, but Jose Maria Gimenez quickly replied for the hosts by heading home from a Koke corner.
Saul compensated for his earlier mistake by nodding in another Koke corner, and then Torres sent the Vicente Calderon into ecstasy by hitting his milestone goal in stoppage time.
It was a return to winning ways for Atleti, whose season had begun to unravel in the last two weeks, drawing at home to Sevilla, exiting the Copa del Rey at the hands of Celta Vigo and then falling three points behind Barcelona in La Liga by losing 2-1 to the Catalans with nine men.
Villarreal eked out a point from a dismal goalless draw at Athletic Bilbao to maintain their challenge for a top-four finish.
In a techy stop-start encounter referee Mario Melero brandished 12 yellow cards and two red as both sides saw out the game with 10 men following the late dismissals of Athletic striker Inaki Williams and Villarreal substitute Daniele Bonera.
The point keeps Villarreal in fourth place, while Athletic remain sixth and stay on course for Europa League football next season.
In Saturday’s late kick-off, Deportivo recorded their fourth consecutive draw as they recorded a 1-1 result away to relegation-battlers Sporting Gijon to remain without a La Liga win since before Christmas.
The home side had won their previous two games to move away from the drop zone and took the lead just after the half-hour mark through a deflected 20-yard strike from midfielder Jony.
Victor Sanchez’s side, though, were level before half-time when Luis Alberto fired in from close range.
In the day’s other game, Rayo Vallecano climbed out of the relegation zone after beating fellow strugglers Las Palmas 2-0.
Miku bundled the ball in after just four minutes to give Rayo the lead, while former Manchester United winger Bebe finished off a classy move in the second half to seal the points.
Malaga cruised to an unusually high scoring 3-0 defeat of Getafe on Friday inspired by Juanpi, to go level with ninth-placed Deportivo La Coruna.
Venezuelan midfielder Juanpi scored the first goal and contributed to another as the three points took his team four clear of 11th-placed Getafe.
The opening goal came in the ninth minute when the 22-year-old classily dribbled past three Getafe defenders before shooting low inside the far post beyond goalkeeper Vicente Guaita.
Christian Atsu, who recently joined Malaga from Chelsea on loan until the end of the season, then added a second goal 15 minutes later.
Anor displayed fine vision to find Charles, and the Brazilian forward crossed for Ghana winger Atsu to score with a routine finish.
In a demonstration of their devastating superiority Malaga’s third goal, and effectively all three points, were secured by half-time.
Guaita was stranded in the 43rd minute so, seizing a fine opportunity, the impressive Charles scored his ninth of the season with a right-footed shot beyond the goalkeeper.