Sainz surrendered the lead from pole position to Max Verstappen, but regained the lead on lap nine because of a DRS pass on the championship leader in the primary corner.
It was a lead that Sainz continued to construct, giving him a big margin to cushion any transient moments of pressure from teammate Charles Leclerc or pressure from Lando Norris late within the race.
Speaking to Sky Sports, the Spaniard said he was keen to finish his time at Ferrari on a high with at the least one race win before moving to Williams for 2025.
“It's only a matter of I feel everyone knew I wanted one other race win with Ferrari. I felt I deserved it too,” Sainz said.
“I rode well all 12 months and gave my all, keeping my motivation high even in difficult circumstances and wanting to present my all for this team.
“I felt like I had done some really good races and I needed to win another. It finally happened and it needed to be in Mexico in front of my family, which is great.
“That doesn't mean I'm not going to try to win more. But it had to happen here.”
Carlos Sainz, Ferrari SF-24
Photo: Dom Romney / Motorsport Images
Sainz said his family's presence on the race and his confidence within the automobile made him feel like “something was brewing” through the weekend in Mexico.
He admitted he made his day difficult by losing a position to Verstappen initially, but most significantly he had the arrogance – and pace – to return the favor to his former team-mate.
“Honestly, it's definitely one of the best feelings in the world. I felt like after Checo they probably supported me,” he added.
“Since I got here to Mexico, I had a sense that victory was possible. I knew my family would come to go to me this weekend. My mother might be present. I knew I hadn't won the race with my mom ahead of me.
“My best friends are here, my dad, and I assumed, 'something might occur this weekend and I even have to make certain I do the whole lot I can to win this race.'
“Even though it was a bit difficult at the beginning, then I managed to hold on to Max and from then on I enjoyed the race.”