Germany international Ozil broke the deadlock against Real Betis on the stroke of half-time and then wrapped up the scoring with his second right at the end.
In between those two strikes, Karim Benzema had put Madrid 2-0 up before Betis pulled a goal back through Jorge Molina's 73rd-minute penalty.
The victory is just what Madrid would have been hoping for heading into a crucial run of fixtures over the next 10 days.
On Wednesday they travel to Germany for the first leg of their Champions League semi-final against Dortmund before then facing local rivals Atletico Madrid at the Vicente Calderon next weekend. Three days after that derby, Jose Mourinho's men play the second leg against Dortmund at the Bernabeu.
It was not all good news for Mourinho though with Marcelo and Luka Modric limping off with injuries.