Suarez Navarro, ranked 42nd in the world, called her 6-4, 4-6, 6-1 triumph over the world number three "one of the most important matches of my life," but it was clear Kuznetsova was well off the form that saw her capture the French Open last year and rise to number two in the world in September.
"It's frustrating, because I know I have the game," said Kuznetsova, who has struggled to get her 2010 season rolling. "I feel great. I do practice, play unbelievable, and then get to the match and I don't do much.
"My thinking is I just need more matches."
Since falling in the fourth round at the Australian Open, Kuznetsova hasn't been able to put many matches together. She lost in the third round at Dubai -- after receiving a first-round bye and advancing from the second round on a walkover.
After breaking Suarez Navarro in the final game of the second set to keep the match alive, Kuznetsova then dropped her serve in the opening game of the third.
Suarez Navarro broke again for a 4-1 lead and saved a break point in the next game as she took a 5-1 lead.
"I think the first two games in the third set were very important," said Suarez Navarro, who said she could sense Kuznetsova's frustration.
When Kuznetsova dumped a forehand into the net on the first point of the next game, she slammed her racquet to the ground in frustration.
She was broken at love to surrender the match.
"I am frustrated," Kuznetsova said. "I mean, I feel good and the ball doesn't go where I want it to go, you know. I play there, and it goes a different way.
"I'm like, OK, I play tennis for 17 years and I still cannot put this little ball in this huge court. It's frustrating."
It was the second year in a row that Kuznetsova fell in the second round here, where the 32 seeded players all receive first-round byes.
Suarez Navarro, who made a splash at the 2009 Australian Open when she ousted Venus Williams in the second round, next faces Hungarian Agnes Szavay, a 6-3, 6-2 winner over Taiwan's Chan Yung-Jan.
"Well, now I have another match," the 21-year-old from Barcelona said. "The other player is very strong. I feel good, I feel confident, so we will see what's going to be in the next match."