Espanyol gave Militao space and the Brazil defender fired a right-foot screamer into the top corner in the 22nd minute at the Santiago Bernabeu.
It was Mbappe's turn in the 47th when he had time to pick a spot in the bottom corner and smash a strike that Marko Dmitrovic could only watch nestle into the net.
Mbappe has seven goals in six games for Madrid this season, including a double in its 2-1 win over Marseille to start the Champions League on Tuesday.
"When you are facing a defence set well inside its area, you have to try from long range," Madrid coach Xabi Alonso said.
"Militao's goal was very good, and Kylian scored in transition. We are taking steps forward and continue to grow."
Madrid's fifth win in as many rounds moved them five points clear of Espanyol and Barcelona, who host fifth-placed Getafe on Sunday.
Elsewhere on Saturday, Girona, who just two seasons ago finished the league in third place, remain pointless and stuck to the bottom of the standings after being humbled 4-0 at home by the promoted Levante, for whom Socceroos goalkeeper Mat Ryan played a full game.
Villarreal fought back for a 2-1 win over 10-man Osasuna, Sevilla beat Alaves 2-1 and Valencia downed 10-man Athletic Bilbao 2-0 to bounce back from a 6-0 thrashing to Barcelona last round.
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