Higuain stepped in for the injured Karim Benzema.
He said: "I recovered from my surgery as soon as I could in order to play as soon as possible. I was looking forward to playing this well and scoring again. I also played the entire game, which will help me reach optimum form.
"This victory allows us to catch up with those in the lead. It was a difficult game that served me to grow more confident and to have more playing time. We have to continue playing as a team because it will lead us to win titles.
"Mourinho congratulated me. Everybody knew I needed this after my injury. I only think about enjoying the ride and focusing on one game at a time.
"Alvaro gave me a perfect pass for my second strike and I did not hesitate to cross it into the goal."