After a tight first half, Casemiro on Wednesday evening opened the scoring with a 57th-minute header from Marco Asensio's cross and Karim Benzema sealed the win in the closing moments of the game, reports Xinhua news agency.
Although Madrid deserved the win for the football they displayed in Valdebebas, Granada had two good penalty claims rejected after Casemiro clearly pulled Yangel Herrera's shirt in the first half and appeared to block a shot with his arm 16 minutes from time.
Getafe and Celta Vigo drew 1-1 earlier on Wednesday. Denis Suarez opened the scoring for the home side with a thumping seventh-minute shot only for Iago Aspas' penalty to cancel it out shortly afterward in a game of few chances.
Wednesday's late games saw Edger Mendez and Deyverson score goals in the 40th and 46th minutes, which saw Deportivo Alaves recover after receiving a third-minute goal scored by Pedro Leon to beat Eibar 2-1.
Finally, Guido Rodriguez's 71st-minute strike game Betis a 1-0 win at home to Cadiz.
Among the games played on Tuesday, Atletico Madrid confirmed its leadership with a 2-0 win away to Real Sociedad, while FC Barcelona won 3-0 away to Valladolid, and Villarreal drew 1-1 at home to Athletic Club Bilbao.