Leipzig were energetic but wasteful early, frequently undoing their good work with poor decision-making in the final third. The hosts were made to pay early in the second half when Diaz opened the scoring. Drafted into the side in place of the injured Jude Bellingham, Diaz danced past five Leipzig defenders before curling an inch-perfect shot inside the far post.
The win was Real Madrid's seventh in seven games this Champions League campaign and puts them in prime position to make it past the last 16 for the fourth straight season. Real travelled to Saxony without England midfielder Bellingham, who injured his ankle in Saturday's 4-0 win over Girona. With first-choice centre-backs Antonio Rudiger, David Alaba and Eder Militao ruled out, coach Carlo Ancelotti opted to continue midfielder Aurelien Tchouameni's stint in central defence.
Real host Leipzig in the Spanish capital on March 6.