The French superstar netted the first and last goals of Real Madrid's 4-1 win over Rayo Vallecano in the Spanish capital on Saturday (Sunday AEST).
Mbappe converted a 14th-minute penalty after Florian Lejeune made a rash tackle of Alvaro Carreras. Lejeune was again to blame when his poor pass was intercepted and led to Mbappe assisting Carreras to make it 2-0. Jude Bellingham slotted the third goal in the 35th.
But modest Rayo took the initiative at the Santiago Bernabeu after halftime, dominating the ball for stretches and finding holes in Madrid's new-look defence.
Sergio Camello poked home a goal in the 51st, moments after Pedro Diaz hit the post and drew the first of several saves from Thibaut Courtois. The Belgium goalkeeper had to bail out Madrid again, parrying more shots by Lejeune and Heorhii Tsitaishvili.
That was too much for many of the home fans, who whistled the dip in performance by Jose Mourinho's side — until Mbappe found the corner in added time.
His double pulled the striker level with Barca's Raphinha and Rayo's Camello with six goals apiece in five rounds.
"I expected the match to go this way, given our (midweek) Champions League experience," Madrid's Portuguese coach Mourinho said.
"The aim was to start strongly and wrap the match up quickly, and we achieved that."
Elsewhere, Roberto Fernandez kept up his strong start by scoring a brace to lead Espanyol to a 2-0 win at Osasuna. Fernandez has five goals in as many games, after the striker scored only seven in the league all last season.
Yassir Zabiri also found the net twice to lead the promoted Racing Santander to a 2-1 home win over Alaves. Zabiri has five goals since joining Racing from Ligue 1 Rennes on loan.
It was a first loss for Alaves, while Athletic Bilbao, another Basque club, drew 1-1 at home with Elche.
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