Mbappe, who had played in a central attacking role since joining from Paris St Germain, went four games without scoring in all competitions before netting the opener against Leganes.
The 25-year-old was moved back to his preferred position on the left and combined well with fellow attacker Vinicius Jr, who set up Mbappe's goal.
"Vinicius and I read each other very well. I've got a great relationship with him and he's a great player," Mbappe told Real Madrid TV after the win.
"I think I put in a good performance. I'm starting to get up to speed with my teammates. I can play in every position and I'm ready to help the team and give my all.
Real are second in the league, four points behind Barcelona, who have played one game more. The leaders drew 2-2 at Celta Vigo on Saturday.
--Reuters--