Mbappé's 33 goals in all competitions since joining Madrid already equals the tally that Cristiano Ronaldo reached in his entire first season for the powerhouse in 2009-10.
"It is very special," Mbappé said about matching Ronaldo's mark with two months to go in this campaign. "We know what he represents for Real Madrid, and he has given me lots of advice. But, as I always say, we have to win titles."
The match between the defending champions and a team trying to stave off relegation was billed as an easy three points for Madrid. It was anything but as Leganes showed much more bite than expected at the Santiago Bernabeu.
After Mbappé put Madrid ahead from the penalty spot in the 32nd minute, Leganes stunned the home crowd by hitting right back after the restart. Left back Valentin Rosier sprinted clear on the right flank and crossed for Óscar Rodríguez, whose poorly hit shot was pushed home by Diego García.
The minnows from southern Madrid did it again in the 41st. This time, Rosier stole the ball from Brahim Díaz and raced down the center of the pitch before he played Rodríguez clear, who squared the ball for Dani Raba to take the lead.
Even though Leganes continued to threaten a third goal, Madrid capitalised on their chances in the second half to turn it around.
Jude Bellingham equalised when he rushed in to finish off a rebound. Mbappé made it a brace from a free kick, slicing the ball through a hole in the defensive barrier and just inside the post after a strict foul call that was protested by Leganes.
Meanwhile Atletico's 1-1 draw at Espanyol left them six points behind the front-runners with nine rounds left after this weekend.
César Azpilicueta put Atletico ahead in the 38th with a spectacular volley of a clearance by an Espanyol defender that fell to him outside the area. The 35-year-old defender celebrated his first career goal in La Liga.
Espanyol pressed in the second half and Javi Puado converted a penalty to level in the 71st after Clement Lenglet pulled down Leandro Cabrera while disputing a cross in the box.
Atletico led the league in January but the wheels have come off in March.
In other results Mikel Oyarzabal and Sergio Gómez scored as Real Sociedad beat last-placed Valladolid 2-1, while Rayo Vallecano won 2-0 at Alaves.
