With four games remaining, Real climbed to 87 points and extended their lead to 14 points over second-placed Barcelona and 16 clear Girona in third.
Real's manager Carlo Ancelotti rested several key players ahead of their Champions League semi-final against Bayern Munich and his side did more than enough to secure the three points.
After dominating the first half, they finally managed to break the deadlock with Diaz first netting a curling shot from the edge of the box in the 51st minute.
Borussia Dortmund's B-team warmed up for Tuesday's semi-final at Paris Saint-Germain with a 5-1 rout of visiting Augsburg. Dortmund's veteran Marco Reus scored one goal and set up another in his first match since it was confirmed he will be leaving his hometown club after a 12-year stint at the end of the season.
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