The German, back with Force India after not racing last year, benefited from being one of the few drivers who started the race on the medium tyre compound to move into the lead after the frontrunners had pitted.
Although he came under pressure from Sebastian Vettel, Sutil managed to stay ahead before he made his first pitstop.
The Force India driver then went on to finish in seventh position.
"I wasn't expecting that but I came back to do better and it was a great feeling to be straight up there," said Sutil. "So I just tried to keep concentrated and use my chance. I was amazed we could be competitive at the front.
"I gained first place back after the first pitstop so the pace was really there. Vettel was probably too close running behind [me and] maybe destroyed his tyres, but the pace was there and that was great to see.
"I knew we were going to lose a few places [in the final stint] because I was on an opposite strategy but nevertheless seventh in first race, to lead quite a lot, it showed what was possible. It's a sign you should never give up and always believe, anything's possible."
Sutil said he had to keep his emotions in check when he realised he was leading the race, but he insisted he was ready for it thanks to his new mindset in his second Formula 1 spell.
"It was nice to see P1 on my board, no question," he added. "But it's very important to keep your emotions under control in the sport. Emotions are not the best to have, when you want to race you want to be successful.
"I think I'm quite good at it now. I saw that as a big day, it was nice, but it's not that I wasn't feeling good in this position.
"When I came back into the sport I thought I'm just coming back if I can do better. I programmed my mind for this kind of position. I know it's just maybe only today, but maybe it will come again and I want to go to the front."
The German said he is now hungry for more.
"We show we are absolutely strong enough to score points and I'm always aiming for my first podium," he said, "for a long time I've wanted to do that.
"Whenever it comes I want to be ready that's a good target for this year, maybe it happens maybe it not but I will push for that."
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