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Zinedine Zidane's defending champions sit second in the table, seven points behind Atletico, who have two games in hand and face Cadiz on Sunday.
Militao was shown a red card in the ninth minute at the Alfredo di Stefano Stadium, with his team already without their injured captain Sergio Ramos and Covid-stricken coach Zinedine Zidane.
Marco Asensio gave Madrid the lead four minutes later but Jose Luis Morales equalised before half-time before Roger Marti made up for missing a penalty by scoring the winner.
Barcelona coach Ronald Koeman had admitted earlier on Saturday his team "have to be realistic" about their chances of overturning Atletico's considerable lead in the table.
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And with Real Madrid slipping up again, it will now take a seismic collapse for Atletico to miss out on repeating their incredible La Liga triumph in 2014.
It also leaves the Champions League as Real Madrid's only obvious chance of a trophy this season after they lost in the Spanish Super Cup semi-finals and went out to Alcoyano in the Copa del Rey. Madrid face Atalanta next month in the Champions League's last 16.
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