The Brazil full-back struck with four minutes of normal time remaining after Dani Parejo's free-kick had cancelled out Cristiano Ronaldo's first-half opener.
The winning goal, which came only four minutes after Parejo's stunning equaliser and followed a missed penalty from Ronaldo, ensured Madrid moved three points clear of Barcelona at the top of La Liga ahead of their derby clash with Espanyol later in the day.
Marcelo was thrilled with his first top-flight goal since October, but more pleased with his side's determination to fight for what could prove a pivotal victory.
"It's impossible to know if the goal will be decisive or not. I'm happy with the three points in a difficult game," he told beIN Sports.
"There are a lot of people who come to the Bernabeu who want to frustrate us, but that's normal. We dug deep into our soul and we've shown who we are. Real Madrid are a great side.
"In the end, we went out running and fighting and we got three important points. I'm happy with the goal but more for the points. It's important that we keep going, step by step, and that we fight until the end.
"We want to win every game we have left. The objective is to go step by step, but with a lot of effort."