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Liverpool forward Diogo Jota held up Diaz's No. 7 shirt to show support for him after scoring the first goal of the match as the 2019-20 champions stayed fourth in the table with 23 points from 10 games.
Manchester United's campaign of woe continued with a 1-0 home loss to Crystal Palace but there were no such troubles for Arsenal who, along with Spurs, closed the gap to leaders City to one point with a rampant 4-0 win at Bournemouth.
New signing Szoboszlai also scored in a 3-0 win at Anfield.
Liverpool snatched a 2-1 win after going a goal and a man behind in the first half.
Axel Disasi cancelled out Luis Diaz's opener for Liverpool.
Leeds defender Rasmus Kristensen's second-half equaliser denied Newcastle the victory that would have all but assured them a place in next season's Champions League.
Arsenal have 73 points from 30 games, six points more than second-place City, who have a game in hand.
Both Arsenal and Manchester City scored 4-1 wins in their respective matches.
A disciplined Real seemed content to sit back against a tame Liverpool who carried little threat for most of the game.
Liverpool's previous biggest win over United was a 7-1 victory in 1895.